Anre6pa H normca, 8, Ns 1 (1969), 5. YAK 51.01:518.5:519.45 …math.nsc.ru/~alglog/01-10/08/08N1-1.pdf · 2010-08-12 · Anre6pa H normca, 8, Ns 1 (1969), 5. YAK 51.01:518.5:519.45

Anre6pa H normca, 8, Ns 1 (1969), 5.

YAK 51.01:518.5:519.45

O C/1O>KHOCTH nPOB/IEMbl TO>KAECTBA

fl/IH KOHEHHO OnPEAE/IEHHblX TPYnn

M.K.BA/1HEB

KaK H3B6CTHO, anropHTMHiecKaH HepaapeuiHMOCTfa npo6neMbi

cTBa ana KOHGHHO onpeneneHHbix rpynn (x.e. rpynn, aaaaHHbix KOHennoft

cHcxeMoii o6paayiomHx H onpeaenflioinHx cooTHouieHHlt) 6wna ycTaHOBneaa

n.C.HoBHKOBWM C 1 II . IloaflHee B.B.BynoM C 2 H , F.XHrMaHOM C 3 D H

AK.BPHTTOHOM 114 H SbinH npennoMceHbi npyme flOKaaarejibCTBa sroro pe -

. Ka»noe as STHX noKaaarenfaCTB ocHOBano Ha neKOTOpoJS KOHCT —

, Koxopaa no nioSoMy peKypcHBHo nepeiHcriHMOMy (Kopone, p.n. )

MHO»ecTBy o CTPOHT KOH6HHO onpefleneHHyro (Kopone, K.O. ) rpynny K , K

npoSneMe TOKflecrBa (Kopoie, n.r.) nna Koropoft aêKTHBHO CBOAHTCH

npoSneMa paapeuiHMOCTH zwa S . flanbHefimee HccjieaoaaHHe STHX KOHCT -

pyxuHH (4>pHflMaH C5I] , KnanxsM C6H, noanaee Byn C73 , BoxyTfa L8~A ) no-

Kaaano, HTO HMeex Mecro TaK»ce 3(t4ieKTHBHaa CBOanMocxi, npo6neMbi TO -

>KnecTBa ana K , K npo6neMe paapeuiHMOCTH ana £> , Hnane roBopn, £

H n.r. ana K , HMeiox onny H ry »e cxeneHb HepaapeuiHMocTH. STOT pe-

, yKaabmaa na cymecTBOBaHHe aosojibHO TOHKOH aepapxHa K.O.

rpynn c HepaapeuiHMoft n.r., B TO xe apeMH He aaeT HHKaKoft HH<j)opMa -

UHH nna KaKoii-jiHSo Knaccn4>HKaunH K.O. rpynn c paapeuiHMOH n.T., -rax.

KBK ace penypcHEHbie MHoxecTBa o6jianaK>T oanoft ( HaHMeHfatueft ) CTene -

Hfaro HepaspefflHMocTM. OnnaKO ana peKypcHBHbix MHOKBCTB (H Boo6me ana

paspeuiHMbix anropHTMHHecKnx npo6neM), B CBOK> onepeflb, raxxe

Hbi paaniiHHbie nepapxHH, xamaasi Ha KOTOPHX CBaaana c HeKoxopbiM

HSHHeM noHSTHa cnoMCHOCTH npo6neMbi (nanpHMep, B xepMHHax cnrnanH3H-

pyiomHx 4>yHKUHH paanirHHoro pona (CM. B.A.TpaxT6H6poT C83) , aepapxHH

A.PjiceropHKKa C 10D npHMHTHBHo pexypcHSHbix MHOHCS CTB H T.a. ). flna

rpynn c paapeuiHMoft npoSneMofi roscaecTBa Taxsce BoaHHKaer Bonpoc 06

M.K.BanHes

HX KJiaccm|)HKamin no CJIO>KHOCXH sxofi npo6neMW. B pa6oxe <I>.KaHHOHHx6

LI H npefljioacena Heicoxopaa aepapxna B xepMHHax fc -KJIBCCOB

flna KOHOHHO nopojKfleHHbix (xopone, K.n. ) rpynn co CHSXHWM HHC -

JIOM onpenenaiomHx cooxHOineHHfi, HMeiomHx paapeuiHMyio n.T.

B aacxoaniefi pa6oxe npennaraexca cyraecxseHHo 6onee xoHKaa aepap-

XHH nna K.O. rpynn no cnoscnocxH npo6nevifai xomnecxsa (B xepMHHax eM-

KOCTHBIX cHrHajiH3Hpyioinnx MaiuHH Tb ropHHra) , Koxopaa B KBKOM-XO CMW -

cne "MonenHpyex* B ananHxejifaHoii cxenemi aHanoraiHyio Hepapxuro ana pe-

MHO»ceCXB.

CymecxBosaHHe xaKoft nepapxHH asnaexca HenocpeacTBGHHbiM cneacx-

xeopeMbi 1, xoHHaa (JiopMynHpOBKa Koxopofi npHBefleHa B § 1. Coaep-

>K3HHe sxofi xeopeMH COCXOHT B XOM, ixo nocxpoenne rpynnbi K. no p.n.

MHOxecxsy 5 Moscex 6wxfa ocymecxaneao xaKHM o6pasoM, HXO n.T. nna

K a H npo6neMa paapemHMocxn ana S csonaxca npyr K flpyry cpaBHH -*)npocxo (c He6onbiiioft eMKOCTHofi cHrHanHSHpyrameft) .

CymecxBeHHyw nacxb Bceft KOHcxpyKUHH cocxaBnaex npHBeaeHHoe B

2,3 nocxpoeniie no p.n. MHoatecxsy £> K.O. rpynnbi TV , o6naflararaell

csoftcxaaMH: 1) JV^ conep«<HT B Kanecxae noarpynnw cBo6on-

rpynny F c o6pa3yioinHMH CL , t> '< 2) nycxb fl & oSoanaHaex non -

rpynny rpynnw F , nopo*neHHyio o6pa3yromHMH CL uCL , L&S \a

-V<- conep»Hx K.n. noarpynny Q^ xaKyro, HXO Q f~l F = fl ,.. .

Hycxb AT - rpynna, HaoMopiJmafl rpynne W, cornacHO H3OMOp4>H3My

Z- : Ct—^-Q , Ct€.N^ . flna rpynnw /< , Koxopaa asnaeTca CBo6oaHbiM

npOH3BeneHH6M rpynn N u. W c o6i>eAHHeHHeM cornacno X- noarpynn/ 5» S

Gtr H Q , . nerKO nOKaaaxb, HXO n.x. nna nefe n npo6neMa Bxo%aeHHH B

nonrpynny Q_ rpynnbi jVV aoao/ibHO npocxo cBoaaxca apyr K flpyry. C

npyrofi cxopoabi, H3 npocxoro saMenaHHa , Koxopoe cnenano

6€ S~*~*~G: Vd. £/?r,n us csoftcxBa 2) rpynnw N^ OHesaaHbiM oSpaaoM

BbixeKaex 3KBHBaneHXHOcxb: L€. S " *• CL GO. G Q r . T-e- npo6neMa paa-

peiuHMocxH ana S npocxo csonnxca K npo6neMe Bxo«neHHa B Q . riosxo-

My fljifl nonyneHHa xeopeMbi, asanorHHHoii xeopeMe 1 (xonbKO c 6onee rpy-

SbiMH oneHKaMH), nocxaxoHHO noKasaxb, HXO npo6neMa BxoxaeHHfl B Q

xax we aocxaxoHHo npocxo cBOflHTca K npo6neMe paspemnMocxH nna 5 .

AHanorHiHbift peaynbxax nonyien B.A.TpaxxeH6poxoM B C12J ,npM 3XOM OH Hcnonbsyex npyryro KOHcxpyKuaro rpynnw K, , HaabiaaeMyioHM KOHcxpyKUHeft HoBHKOBa-Byna.

O cnojKnocTH npoSneMbi Townecrsa n.ns rpynn

HeKOTOpwfi cnoco6 nocxpoeHHa rpynnw .A/̂ , KOTOPHH MOJKHO HseneHb us

pa6oTbi XHrMana C31I , paccMorpea KnanxsMOM B C6 D . HM noKaaano, HTO

npoSneMa BxojKneHHfl B Q 3<}>4>eKTHBHO CBOZIHTCH K npo6neMe paapeuiHMOc-

TH ana S • OAHaKo, BBnny cBoeft rpoMosaicocTH, KOHCTpyKuna

ManonpnroAHa Ann nojiyneHiia oiieHKH CJIOXHOCTH SToro cseAeHHa. OoaTOMy

nonyieHHa Hy«Hbix OUBHOK B aacToaineft pafiore MW CTPOHM npyryio

rpyimbi ^V . onnpaacfa Ha OAHy (necymecTBeHHO HaMeneHHyio)

H3 npeAHAymeii pa6orbi tl 133 . AoKaaarenfaCTBo TeopeMH 1

aaaepuiaeTca TOFAB B § 4 nocrpoeHHeM rpynnu K necKonfaKO 6onee cno-/ *)

XHUM cnoco6oM, HSM Kf .

KpOMe Toro, B § 1 6yA6T noKaaano, HTO rontKO Ha HajiHHHa oueaoK,

o KOTOpbix roBOpHTca B reopeMS 1, oneHt npocTO BwreKaex TaSnaiHaa

npoSneMH paapeuiHMOCTH AJia S n npo6neMH ToxtaocTsa ana

K<- npyr K npyry. 3ro naer OTBBT aa Bonpoc, nocTasneKHbitt

HOM B C53 .

§ 1. OcaoBHbie onpeAeneHHs, ({KDpiviynHpoBKa H o6cy>KaeHHe

peaynfaraTOB, HeKOxopwe oSraHe

1. AaflHM cnatajia HeoSxonHMwe onpeneneHHa.

OnPEAEJIEHHE 1 C9H . EMKOcTHoft cHrHannaiipyioineii MaiiiHHbi Tbio-

pHHra 7~ 6yaeM HasHBart (JiyHKunio S_(W^ • Koropaa pasna nacny aieen,

HcnonbayeMbix MauiHHOft T npn nepepaSoTKe c/ioea W . ecna MauiHHa

H He onpenenena B HPOTHBHOM cnyiae.

Iwl 4 nrae I W l o6o3HaiaeT A/iHHy cnosa \fj .

Ana Sr (n.) coxpaaHM HasBaHHe eMKOCTHofi CHrHanHanpyioiHeH. B

* A o 6 a B n e H O n p n K O p p e K T y p e . FIocTpoeHHe rpynnw K ̂HCXOAHT H3 HeKoroporo nHo<J>aHTOBO-noKa3aTejifaHoro npencTaBJieHHH p.n.

nonHHOM c uenwMH KosiJxjiHUHeHTaMH. Ilpn STOM HHCJIO o6pa3yioinHX n HHCHOonpeflenaroinHX cooTHOiueHHfl rpynnu K ^ orpanHneHbi caepxy HeKOTOpwMH

, aaBHcaniHMH or creneHji nonHHOMa P H Hiicna nepeMeHHbix,B P, . JlerKO BHneTb, HTO nna Kaamoro p.n. MHOHcecTaa S

npeacraBneHae MOHCHO Bbi6paTb raKHM o6paBOM, HTO yiacTByiomHH B HGM nonHHOM HMeer orpaHHieHHBie csepxy He-

M.K.BajiHeB

CHrHanHSHpyromHe HMBHHO xaxoro pona 6yayx ynoxpe6naxbca

B KanecTBe jcpuxepHa CJIOJKHOCXH anropiixMHHecKnx npofijiSM.

Hapaay c oSbiHHHM noHSTHeM MamnHH TbiopHHra B aanbHeftiueM 6y-

nex ynoxpeSnaxsca xaK>Ke noHaxae MaiiiHHbi TbiopHHra c opaicynoM. HanoM-

HHM 3TO nonaxHe, He BAasaacb B ero iioflpoSHoe (JiopManfaHoe onHcaHHe(xo—

onpeneneHae CM. ASBHC CHU ). Ilycxb /~ - npenmcax, onpeneneHHun

na MHcmecxse CJIOB B HexoxopoM anijmBHxe £ . MauiHHa TfaropHHra 7" ( c

r -opaKynoivt) , KpoMe oSbiHHbix BHyrpeHHHx COCTOHHHS (r.e. cocTOflHHfi,

HaXOHHCb B KOTOpblX OHa MO»6T HHTBTb, HHCaTfa, CflBHraTbCH, H3M6HHXb CO-

cxoaHHe), o6nanaex cneuHajibHbiM cocxoaHneM Q,y. (BonpocHxenbHoe cocxo—

flHHe). Oonaflaa B cocrosHHe On i MauratHa nepexonnx aa OJIHH xaKX B oa-

HO H3 AByx BbiaeneHHbix COCXOHHHH Qo'î B 3aBHCHMOCTM °T TOFO, neMy

paBHO anaieHHe npenHKara I" Ha cnoBe VV^, , asnaiomeMCH npoeKUHeft B2^

anij)aBHx 2j cnosa W , aanncaHHoro na nenxe (B SXOM cnynae 6yneM

roBOpHTb, HTO cnenan aanpoc opaxyny o cnoae Wv ).£u

AnanorHKHO xoviy, KBK sxo caenaao Bbiiiie ana oSbiHHbix MauiHH Tbio-

pHHra, MOJKHO onpeaenHXfa noHflrne eMKOcTHofl cHrHanHSHpyromeS xaKJKe H

MauiHH c opaxynoM.

OriPEflE/IEHHE 2.EMKOGTHoii cHrHann3npyK)ineJi MaiiiHHbi c

6yneM Maabiaaxb (JiyHKmiio & (W) , Koropaa pasna HHcny aneeK, ncnonb -... ' r

ayeMbix MamHHOft / npH nepepa6oxKe CJIOBB W i ecnH MauiHHa ocxanaB-

nHBaexca, H ne onpeaeneHa — B HPOXHBHOM cnynae.

OnPEflEJIEHHE 3. ByaeM rosopHxb, HXO npenHKax /"" csonHTca c

cnrHanH3npyK)inefi V^Wj K npenHKary r , ecjin cymecxByex

MamHHa c opaxynoM I , BbiiHcnaromaa npeaHKax f~ H xaKaa, HTO

33BHCHMO OX 5 CXenBHfa H HHCJ1O nepeM8HHbIX. A HM6HHO X3KO -

BbiM 6ynex npeacxaBneHHe 3^Cf,... ,JCp PCZ.,^,^,...^^^} — O , rae

LL - p.n. MHOKecxBO nap naxypanfaHbix HHCGJI, ynHBepcanbHoe ana acexp.n. MHOjKecxs, £, - HOMep MHOJKecxsa S B cooxBexcxByromefi HyMepa-UHH p.n. MHoacecxB. Oxcrofla aawiroHaeM, HTO cymecxayiox HaxypajifaHbie HH-cna Cl H Z, xaKHe, HTO ana nio6oro p.n. MHOJKecxsa S Moxex 6bixb acj)-4>eKxnBHO nocxpoena rpynna /^ , nna Koxopoft Btinonnaexca xeopeMa 1 H

Koxopas HMeex He 6onee new q o6pa3yK>wnx H He 6onee IBM % onpeae -naromHx cooxHouieHEft. '

rtpHMSHaa K rpynne K^ KOHCxpyKunro r.XHrMana, B. H X.HeftMaaOB(CM. Kypoui CIS I] , cxp. 247-249), nonyiaeM rpynny c AByMH o6paayroinH-MK H He Sonee HOM T. onpenenaromHMH cooxHomeHHHMH, nna Koxopoil MO-»CHO noKaaaxb, HXO n.x. ana nee HMeex xy «e cxeneab HepaapeuiHMocxH,HXO H MHOJK6CXBO S

O CJKMKHOCTH npoSjieMw ToxcflecTBa ana rpynn

B aanbHefimeM Hac 6yner HHTepecoBaTb sonpoc o CHOHCHOCTH cseae -

HHH npyr K apyry anropHTMHiecKHx npo6neM cnenyiomHx Tpex THROB: npo6-

Jiewa paape UIHMOC TH ana p.n. MHowecTB uarypanbHux incen, saAaHHbix B

ynapaoM an$aBHTe { 1 } , npo6neMa ToacaecTaa flna K.O. rpynn H npo6neMa

Bx'oxaeHHfl B HSKOTOpyio nonrpynny K.O. rpynnu.

Kaacnoft HS STHX npo6neM cooTBBTCTByeT npenHxax, ecTecTBeHHMM

o6paaOM onpeneneHHbiii aa TOM «e MHo«ecTBe, HTO H AaHHaa npo6neMa;

roBOpa o CBOflHMOcxH oflHoft npo6;ieMbi K apyroft, 6yneM HMert> B saay

CBOAHMOCTb COOTB6TCTBylOmHX npeaHKHTOB.

KpOMe Toro, H8M HHorzia noHano6HTCH 6onee cno xa.au npo6neMa, HO

npo6neMa BxoxcaeHHa. HM6RHO, nycxb aaaa K.O. rpynna 6- H aeKOTOpaa

66 nonrpynna H c o6pa3yiomHMH h. ., /~L-,... . Torna TpeSyexcs no npo-

HSBonbHOMy cnoBy W H3 rpynnbi [j onpeaenRTb, npHHannejKHT JIH W K

H , H ecjiii npuHaane^KHT, TO nonyHKTb KaKoe-nH6o npeacraBneHae nna

W B oSpaayromnx /1^,/I2, ____ TaKyro npoSnewy B aanbHettuieM 6yneM Ha-

cHJibHoft npo6neMoft axoxneiuia B H . B nanbHeflmeM, Koraa STO

cneunanbHo He orosapHBaeTca, non BxojKfleHHeM neKOTopoft 6yxBbi , B

cnoBO 6yaeM noHHMaTb TaK>Ke axo>KfleHne 6yKBbi ±>

2. OcHOBHyro nacrb HacxoHmeft paSorbi coTasnaeT

cjienyromefl xeopeMbi.

TEOPEMA 1 . f l n a n i o 6 o r o p e K y p C H B H o ne-

p e i H c n H M o r o M H o w e c T B a S c y m e c T B y -

e T K o a e i H o o n p e n e n e H H a a r p y n n a /C"^, ana

K O T O . p o f l B b i n o n H e H b i y c n o B H f l ' :

1 ) n p o 6 n e M a p a s p e u i H M O C T H A n a S

C B O f l H T C H K n p o 6 n e M e T o a c A e c T s a A n H

Kr c e w K O C T H o f t c H r a a / i H S H p y i o u i e f i V(n.)=n.

c a a n p o c o M o p a s e H C T B e e a n H H u e o a —

H O T O c n o B a a. n u H u ri •

2 ) n p o 6 n e M a T o a c a e c T B a f lna K ,. c B o -

a H T C f l K n p o Q n e M e p a a p e u i H M o c T H ana

> c e M K O C T H o f t C H T H a n H a H p y i o i n e f t

c a a n p o c a M H o H H c n a x , He 6 o n b m H x

I B M | W l .

3. Kax BHflHM, reopeMa 1 oueHHBaeT ssaHMHyio cno>KHOcTb S K npo-

6neMbi TOJKfleCTBa ana K ^ • KpoMe roro, ecna S - peKypcHBHOe MHO -

10 M.K.BanH6B

>KecTBO, TO n.T. nna AC paapeuiHMa, H reopeMa nosBonaer nojiyniiTfa Ana

Hee "a6cojiK>THbie* ouenKH CJIOHCHOCTH.

B caMOM nene, MauiHHa c f -opasynoM, BbiHHcnaioinaa npeflHKax r ,

B TOM cjiynae, Korna /" - 3<J>(J>eKTHBHbiH npeamsaT, Moxcer 6wTb nerico

nepecTpoena B o6biiHyio MauiHHy, TaiOKe BHHHcnaiomyio /"J (c acnonbao -

o6bIHHOft MaUlHHH TbIOpHHra 7" , BHHHCJISIOmeft /" ) . UplH 3TOM

rex *HeanropHTMHHecKnx' T8KTOB, Korna MauiHHa o6pamaeTca K

opaKyny, aoaaa MauiHHa BbmonHaeT pa6oTy ManiHHbi 7" Haa aanpauiHBae-

MWM cnoBOM. HcnonbayH STO aaMeiaHne, as TeopeMbi 1 nerno nonyiaex-

ca

TEOPEMA 2 . A n a K a x c a o r o p e K y p c a a H o -

r o M H O s < e c T B a £ [ c y r a e c T B y e r K.O. r p y n -

n a / < , a n a K O T O p o S B b i n o n a e H b i y c n o B H a :

1 ) a n a n i o S o f i M a u i H H b i T b R a p a H r a J~ ,

p e i u a w m e H n p o S n e M y T o ^ n e c T B a a n si K ,

c y m e c T s y e T M a u i H H a 7~. i n a K O T O p o f t

p a a p e u i H M o S H n n a K O T O p o K

Sr (n.) ^ S

2 ) a n a n w 6 o H M a u i H H b i T " , n a K o x o p o f t

p a a p e u i H M o 5 . c y m e c T B y e T M a u i H H a 7~2 ,

p e m a r o m a a n p o 6 n e M y t o w a e c T B a n n a

AC H n n a K O T O p o f i

2

TeopeMa 2 noKaabiaaeT, HTO tiepapxHs peKypcHBHHx MHOJKBCTB no

cnojKHOCTH (B TepMHHax eMKocTHbix cHrHanHanpyioinHx THna ST (n) ) non-

nepeHocHTca na K.O. rpyrnibi, HaHHHaa c CHrHanHSHpyiomnx, pacTy-y

no nopaflKy KaK n. , H Bbime, Tax icax npn STOM ycnosHH S n n.T.

/( HM6IOT OflHHaKOBbie BepXHHe H HHXCHH6 OH6HKH CJIO5KHOCTH. BAj

, Ha TeopeMbi 2 H H3 cymecTBoaaHHa cooTBeTCTByromHX npHMe -

poB peKypcHBHbix MHOKBCTB (CM. B.A.TpaxTeHSpOT C93 ) HenocpeacTBeH-

HO BwreKaioT cneayronuie yTBepacaeHHa (pent, seaae HneT o eMKocTHbix

CHrHanHanpyioniHX rnna S_ (n) ).

CHEACTBHE 1 . F l y c T t V - n p o H S B O j i b n a a pe-

K y p c H B H a a 4 > y H K U H a T a K a a , H T O 1 ) c y -

_ OcnojKHOcTH npo6neMbi TOscaecTBa ana rpynn 1 1

m e c T B y e x M a u i H H a T f a i o p H H r a , a n a K O -

T o p o ft <^ a a n a e T c a e M K o c T H O f t c H r H a -ry

n i i a H p y i o m e f t , H 2 ) ^P(ri) 9- n . T o r n a c y m e

c T B y e T K.O. r p y n n a K ^ , x a K a H, H T O

1) n K) 6 a a M a m H H a T b r o p H H r a , p e u i a i o -

m a a H.T. a n a /< ,- , H' M e e T e M K O c T H y r o c H -

r H a n H S H p y i o i n y i o , K o T o p a a no n o p a n. K y

n e M e H b m e H e M <f(7~i);

2) c y m e c T B y e r M a m n H a , p e u i a i o m a a

n . T . f l j i a K ^ c e M K O C T H O f t c H r H a J i H a n p y -

KJ in e ft <P(rL) .

CÊflCTBHE 2. n y c T b ^ - n p o H a s o j i f a H a a

p e K y p c H B H a a n s y M e c T H a a <{) y H K u H a .

T o r n a c y i n e c T B y e T K.O. r p y n n a K ̂ , n n a

K o T o p o H B b i n o n n e H O y c j i o a n e : ana J IK>-

6 o f i M a u i H H b i 7 ~ , p e u i a i o i n e f t n.T. ana K ̂ , c y -7-/m e c T B y e r M a ui n H a / , T a K M e p e m a r o u i a a

a x y n p o 6 n . e M y , n p n H 6 M a n a a o c r a r o H H O

Sr Crr; ^ T: (ntsTi

CnencTBHe 1 noKaabiBaex, HTO cyraecTByiOT K.O. rpynnfai, ana KOTO -

ptix npoSneMa ro*aecTBa HMeex onTXManbHyio no nopaaxy cHrHanH3Hpyio -

myio. CnencTBHe 2, Haofiopor, noKaabiBaer, HTO cymecTByroT K.O. rpynnu

c npo6neMoii TowaecTBa, eMKOCTHaa cHrnanHSHpyiomaa ana Koropoft acer -

aa aonycKaeT cymecTBeHHoe ynynuieHHe. Bonee Toro, HS o6mHx cob6pa*e-

HHfi (PM. LQH ) BbixeKaeT, HTO cneacTBne 2 HMeeT Mecxo H npn nK>6oM

apyroM pasyMHOM Bti6ope HOHBTHH curHanHaHpyioineft (ana cnrHanH3npyio -

IHHX speMeHH, pe>KHMa H acex apyrux, yaoBneTBOpaiomax axcHOMaM BJIKD -

Ma) .

4. Ceftnac noKaJKSM , KBK HS reopeMhi 1 MO»HO nonyHHTfa yTBepacae-

HHe o Ta6nHHHoft cBOflHMOCTH apyr K npyry npo6neMbi paspeuiHMOCTH ana

S H npo6neMH ToacaecTBa ana K „ .j

BO3MO>KHOcTb OHeBHnHbiM o6pa3OM BbixeKaex H3 cjienyramefi neM-

Mbi o6inero xapaKrepa.

J1EMMA 1.1. r i y c T f a n p e a H K a r / T Haa M H o -

2 K 6 C T B O M c n o B B a n f y a & H T e 2 c B o a n T -

12 M.K.BajineB

c a K n p e n a i c a x y / " ' B a a M H O S C B C X B O M

c n o a B a j i < J > a B H T e 2 c n o M o m b i o M a -

u i H H b i c o p a i c y n o M , C H r H a n n a H p y i o m a s

K O T O p O ft M 3 > K O p H p y e X C H 3 < ] ) 4 ) e K X H B H O E

$ y H K H H e f t V . T o r n a / ^ C B O A H X C S K f~ T a -

6 n H H H o.

IToKaxeM cnpaBennHBOCTb JIOMMHI 1.1. Flo onpeneneHHio xa6nHHHofi

CBOAHMOCTH xpe6yeTca yicaaaTb anropHTM, Koxopufi HO nio6oMy cnosy W

B an$aBHTe S^ Aaex: a) KOHxponbHbifi Koprex <U.f, U2 ..... ££<fw. > ,

roe U/,U.i,...,aK(wf cnoaa B amjmBHxe £ , H 6) 6yneay

or K. (W) nepeMeHHux xaicyK), ITO anaieHHe /"^ ^\V) coanaaaeT co

HHBM -f (r<U,f), r (U.^, . ••>f~(LtKfW)))- BaSepeM B Kanecxse

KOpxe»;a MHOxcecxso Bcex cnoa HJIHHH He 6onee H@M V(WJ B

(4>HKCHpyH npoH3BOJibHbift nopjmoic), a (JiyHKUHM -^ onpenenKM

oSpasoM. Tlycrb «5/,&2, . . . ,GX(W,>- HSKOTOpbift na6op Ha nyneft H

HHU. Ana onpefleneHsra anaseHHa j- (€>f ,<52,.. .,6^. . ) nocxynnM xaK. Bw-

AenHM Ha neare MaiiiHHbi ynacroK nnHHM V>(V/) H aanycxHM MauiuHy nan

CJIOBOM W . Korna MaiiiHHa npaxoanx B cocxoaKKe O^ , aanpaiiiHBaa o

cnoae LL- , cxaBHM efe B cocToaHHe Q&_ , sacxaanafl pa6oxarb aanbiue;

npH SXOM ace apeMfl Ha6nionaeM sa TBM, Hxo6w, c OAHOH cxopOHbi, rones-

KB MainHHw He Bbixoflnna aa npeaenbi BMfleneHHoro ynacxKa H,C npyroft

CTOpOHu,. iToSbi oHa He aauHKnHnacb aayxpH axoro yiacxKa (axo aenaex —

CH 9c|j(})eKXHBHo c noMorabro ciera HHcna XBKTOB) . ECHH xaKHM o6paaoM

K pesynbraxKBHoft ocxaHOBKe MauiHHbi c OTBSTOM 0 HJIH 1 , xo

f (Of, C>2,...,GK(Wi) nonoxHM pasHbiM sxoMy peaynbxaxy, B npoinx

cnyiaax -f(6/,C>2,. .., &K(wl ) MOMCHO onpeaenHXb npOHSBonbHMM o6pasoM.

HenocpeacTseBHO HO nocTpoeraui BHOHO, HXO yKaaaHHbie Kopxesc H Synesa

4yaKnHH yaosnexBOpaiox ycno»BsiM RS onpeneneHHH xa6nHHHofi CBOAHMOCTH.

3AME4AHHE. IlycTb saKHM-TO ecxecxseHHtiM cnoco6oM onpeaene -

HO noHflxne OIOJKHOCTH xafiriHiHott caoflKMOCTH oflHoro npeaHxara K apyro -

My (HanpHwep, nepes cHrHajiH3npyioinyio ManiHHbi TbiopHHra, no cnosy \

Koprex <.u./,C£i,...,ti^.^)7'Ta. 6yneay (JiyHKnaro j- ). AerKO

HXO aoxaaaxejibcxBO neMMbi I.I. B aeftcxBHTenbHOcxH ycxaKaBJiH —

aaex 6onee cHnbHoc yxaepxaeHHe. A HMSHHO, ecnH aaaaua Mauinna 7"_ c

opaxynoM, csoflarnaH ^ K /" , xo no (JiyHitnHH V> , Maacopapyioineft

HanHaHpyiontyio MauiHHbi T , MOXCRO ycxanosEXb oneHKH CTIOJKHOCXH xaxace

O CJIOXHOCTH npo6;ieMbi TomaecTBa ons rpynn 13

H nna Ta6nHiHo» CBOAHMOCTH r K T . HanpHMep, SCJIH V7 - HPHMHTHB-

HO peicypcHBHafl 4>yHKUHa, TO FI HPHMHTHBHO pesypcHBHO csoflHTCfl K r

Til T.fl.

5. B aaKJiroieHHe sxoro naparpa<J>a npHBeaew HeKOTOpwe HaaecTHHe

reopeTHKo-rpynnoBbie peaynfaraTbi, KOTOpfaie 6yayr HcnonsaoBaHbi B cneny—

KOTHX naparpa4>ax.

Caanana BBeneM HeKoropbie o6o3HaneHHfl . Fpynny c o6pa3yK>mnMH

Of , Q£,--- H onpenenaioinHMH cooTHomeHHHMH &f = £?2 = . . . = / 6yaeM

o6o3HaHarfa nepes \QfQy, •••' /2/—^2=i--.= /i • ECJIH H H /^ - nonr

rpynnw rpynnw G i ro{H,f<} 6yaeT o6o3HaiaTi> nonrpynny B &r no-

pOKneHHyK) nonrpynnaMH t-\ K . ECJIH &• - rpynna c oSpaayromHMH

C^1,qz,... H Q/,Ki,. . . - cnoBa B o6pasyioinHx fy,y2,-~', tf, tz , • - • •

TO nepes |i7, 'ti,'t . . . ', G ,~ R. =...:=/} 6yaeM oSosHanaTb rpynny, no -

nynaeMyra as C ao6aBneHH6M o6pa3yiomHx •&.,£... H onpenensHoinHx co -

OTHOUieHHfi /S = / = . . .= / . ECJIH npH 3TOM ao6aBJIfleMbie COOTHOUieHHfl

t> a-- 1; = ^- (a/;)£. U CY L/ Li w ~l U Lt]

f,2,...)- cnoBa rpynnti 6- , TO 6yneM roBOpnTfa, HTO ~t- - npo-

SyKBbi Haa rpynnofi Cr . Ecna f. saaaeT HSOMOP^HSM noarpynnu

/7 . , nopo>KfleHHoft cnoBaMH <2/.-, j—1,2, . . . , Ha neKOTOpyro nonrpynny

S3 G t TO /• 6yneM HasbiBaTb npasanbHOft npoxonnoft SyKsoft C l ] .LB § 2 HSMH 6yaex RcnonbsoBaHa cneayiomaH neMMa, Kacaiomaiicfl

rpynn c npasunbRbiMK npoxoAHbiMH 6yKBaMH.

HEMMA 1.2. (BPHTTOH C43 ). 0 y c T b A/= { G , t,f,tz,... ',

tiaijtl = ^Hy;' i>.j=t.2,~-} - r p y n n a c n p a B H -

j i b H M M H n p o x o f l H b i M H S y K B a M H ^ ^ , ^ - , . . . n a a

C r . I l y c T b W - c n o B O B o 6 p a a y i o m H x

r p y n n h i / - / H t W p a a n o e a H H H u e B / - / . T o r -

n a n n 6 o W - c n o a o B - o 6 p a s y i o m H x r p y n —

n w £ ^ « W P B B H O 1 B £ - , n H 6 o W c o a e p j K H T

O H H O H 3 n o f l c n o a t~~;' at; ,CL£.A; , t ; CLt~: .Ct Li Li L> t/

r a e # - c n o a o H 3 ^

KpoMe neMMbi BpHTTona, HBM noHaao6HTCH cneayiomHe

KOTOpbie KacaraTca CBo6oaHbix npoHSBeaeHHfi rpynn c o6i>eaHHeHHO& noarpyn-

noft H nerKO BbireKaiOT us reopeMbi o KaaoHHiecKoti 4>opMe ana. TaKHX

(CM. Kypoui C 15] ).

/IEMMA 1.3. (X.HeHMaa). H y c x f a ^ " - C B o 6 o f l H o e

14 M.K.BanneB

n p O H S B e n e H H e r p y n n / ? n E> c o 6 i > e f l H H e H -

H o ft aonrpynno&L . n y c T b C H D ~ n o a -

r p y n n H r p y n n / ? H B T a K H e, H T o Ci~i[_=DnL, — M.

T o r A a 1) n o A r p y n n a {C,Z7} e c T b c B o 6 o n

Hoe n p o n 3 B e a e H n e r p y n n C H JJ c o 6 i e -

flHHeHHOft n o n r p y n n o f t N n 2 ) { C,D\ ft =• C .

AEMMA 1.4. II y c T fa F - c B o 6 o a H o e npo -

H S B e n e H H e r p y n n £7-^ H C^ c o 6 i e f l H H e H H -

O M H 3 O M O p 4 > H b i x n o n r p y n n /?y H f l ( f l f — non-

rpynna HS £^ , fl. - nonrpynna HS Cr ) . T o r a a J i i o 6 o e

c n O B o W H 3 G p a a H O c n o s y B n o p M a j i f a -

H o f t 4> o p M e Wx W2 • • • W^ , r a e

a) w^ e Gf H « H w^ e ^2 ;B) w- n W - i , ne n e j K B T o f l H O B p e M e H H O H H

L if "• I

HH B

c) e c n n ^ ? / , TO w<; 4 ^, . Vv^

ecnn y/ = / , T O

cnoaa as £r. >6Z-. (i—1,2 ..... x)- cnosa us Cr , nw6oe as u.- , sa

HH6M, 6bJTfa MOW6T, ZZ^ H i/ , OTHHIHO OT eflHHHUbl. Ha3OB€M JIK>6oe H3

ti/ MHOHcHTenew caiosa W . Cnoso B nopManbHofl <J>opMe, paBHoe W ,

, Mower 6biTb nonyneao cneayKDmHM o6pa3OM: cpena MHOwHTeneft

paswcKHBaeM MHoacHTejib, npHHannejKamHfi o6ieanHeHHOfl..,...,y

nonrpynne, H, ecnn TaKOsoft Haflflerca (nna onpeneneHHocTH nycxfa OH npn-

rpynne Crt ) > ero saMeHaeM C/IOBOM rpynnu £• , paBHWM ewy,

TBKHM o6paaoM CJIOBO c MenbiuHM HHCJIOM MHoxiiTeneft n r.fl.

yKaaaHHufl cnoco6 nonyneHna HopManbHoft (jiopMbi 6yneM B

Hasbiaaxb cnoco6oM coxpameHHa HHcna

Ha BwiiiecKaaaHHoro OHeBHflHbiM o6pasoM

JIEMMA 1.5. I l y c T b ^ ' - r p y n n a , H S O M O P C } )

n a a r p y n n e ^ r n p « H 3 o w o p i } ) H 3 M e : C ' — •— a ' ,

£f €• Cr ( ciHTaew, HTO Cr ̂ G == r ) . T o r n a n p H B e a e -

H H 6 K H O p M B J I b H O f t ( J ) O p M e C H O B P p y n -

n u {£r, G , CL= &,', CLG. fl\7 - H e K O x o p a a n o f l -

r p y n n a r p y n n u £ r , M O « ; e T 6 b i x f a n p o a e -

a e H o 6 e a n c n o n b 3 O B a H B f l a o n o n H H -

O C/IOJKHOCXH npoSneMbi xcmaecxaa ana rpynn 15

x e n fa H bi x a H e e K n a M a m H H e c o p a K y

ji o M , p e u i a r a m H M n p o 6 n e M y B x o j K a e H H H

B n o a r p y n n y / 7 a n a c n o B r p y n n M G

8 2. OUGHKH CJIOWHOCXH HeKoxopwx anropnxMHHecKHX

npo6neM, CBaaaHHtix c rpynnofl M

1. KaK yxce yKasHBanocb BO BBeaeHHH, ocHOBHyio nacxb KOHcrpyKUHH

rpynnw Kr cocxaanaex nocxpoenne no p.n. MHOMcecxay ^ K-°- rpynnw//",

coaepKamefl cBo6oaHyio rpynny c o6pa3yiomHMH Ci,u H K.n. noarpynny Q^

H ana KOTopoft cnpaaeanHBbi cneayiomRe flBa npeanonceHHH.

nPEfl/lO^CEHHE 1 . t e S x o r a a H x o n f a K O x o r -

a a , K o r a a oTi'&cLt'€ Q^ .snPEflJIO)KEHHE 2 . H p o 6 n e M a B x o M c a e H H H B

n o a r p y n n y S t i n a c n o B r p y n n w NC p e m a -

e x c a H a M a u i H H e c S ~° p a K y n o M c c u r -

H a n H 3 H p y i o m e H , H e 6 o n f a u i e f t , H B M Iwl , c

s a n p o c a M H o n n c n a x , He 6 o n b in H x H e M

2. nocxpoeHHe rpyraibi N npoBOflHxca, Hcxoaa us $HKcupoBaHHoro

npencxaBneHHH ana p.n. MHoxcecxBa £ :

c x.,. . ., :C npo6eraiox MHOHCBCXBO nenwx nncen H TffL — KOHIIOHK-

UHa ajieMeHxapHbix (JiopMyn onnoro HS BHHOB:

ac—C (L=0,1,...,m.,C=0,±1,±'2.>...), ̂ =X- (O^LJ^ m),

Xm-1xi+.Xj=JcK ,xL-Xj=xK (0< K< i<j <m), ozm=^ 2

BOSMOWHOCXB nonyneHHfl xaxoro npeacraBneHHa paccMaxpHBanacb B

OKOHiaxenfaHO nocxpoeHHe W 6ynex aaBepuieHo B § 3. A B SXOM

naparpa<t>e paccMOxpHM oaHy KOHKpexnyio rpynny M , xoxopaa

HecymecTBeHHofl MOflHtJiiiKauHeft rpynnw M , oScyMcaaaiueftca B C 13] . Flpn

SXOM see yxsepxcaeHHa, noKasaHHwe B C13H ana rpynn bi M , c cooxaex -

H3M6HeHHflMH nepenocaxca H Ha rpynny M

CacU oSosHanaex aenyio nacxb HHcna X. .

16

3. OnHcaane rpynnbi M yno6no R&tb no

1) FlycTb £ = {a^.a^c,,^,^,^ ..... aW^n.Cm}

CBoSonnaa rpynna.

2) ^ nonyiaerca noSaBneHHeM K C- o6pa3yiomHx t>o,'t1,...,t>rn-& on

penenaiomHx cooTHOmeHHft:

6) £0,£ .,..., t^KOMMyrnpyioT co sceMH ocTanfaHbiMH SyKBaMH rpynnbi

.

3) M nojiynaercfl no6aBneHneM K £r oSpasyromax Ct, <£//£•

<i

a)

dTa.nd=Li r i . i * \ 2

tTt fTT- *

6) cL KOMMyrHpyer co sceMH ocTanbHbiMH 6yKBaMH us & ;

v^ c/ '̂K = ^^^ ;r) ~t--.j KOMMyTHpyer c ^ H co BCBMH ocxanfaHbiMH 6yKaaMH H3& .

LI K KJ 0 _LB nanfaHeftiueM «iacTO BMecro SyKB a.fflvo,t., 6yaeM nacarfa npocro

&,&,£ . IloHTH SyKBanbHbiM BocnpouaBeneHiieM flOKaaaTenfaCTBa npen -

JIOWBHHH 1 us § 3 pa6oTbi C13H noKaabmaeTca, HTO 6yKBM t/Oj't,t,.,t't

aajiHK)Tca npaBHnbHbiMH npoxonHHMH 6yKBaMH nan Cr , 6yKBH d •&-£.-/ LJK

npaBHjibHHMH npoxoanbiMH 6yKBaMH Haa (} ; H ,

HO, HMeex MecTO neMMa (H==>K oaHanaeT, HTO H BKJiaAbiBae-rca B/^) :

HEMMA 2.1. G =3&I==1>M.

4. BseneM HeKOTOpwe oSoaHaneHna (ananorHHHbie xew, Koxopwe aae-

ilSHH B Cl3j .

a) rtycTfa < 0^0,^C.,... ,Xfrl> - uenoHHcneHHbifl BSKTOP. O6osHaHHM

H nepeaa.,^^ ..... ̂ - C.OBO ^...^^/oc^ ..... ̂ >"6) O6o3HaiHM nepea ft nonrpynny B 0 , noposcneHHyKf BCGMH

B) IlycTfa X - MHOKecTBo BeKTOpOB. Torna fly 6yfl6T o6o3HanaTb

O CJIOKHOCTH npoSneMM Toa<aecTBa ana rpynn 17

noarpynny B £/ , nopojKneHHylo TGMH CL, y flna KOTOpux

^X i 7 ,X / , .. .,X /T1 > € X . ECJIH X - MHOW6CTBO HCTHHHOCTH (JWpMyJIH A* ,

T.e. MHO>KecTBo Bcex BeKTOpoB < X^ , ,X / , . . . ,Xrrl >, ynoBneTBOpaiomHx A" , TO

BM6CTO_

r) AJIH aneMBHTapHbix tjiopMyji BMGCTO ft - BBeneM cneuHanbuue 060—

. HMOHHO, fljia (Jiopwyn BHfla: X^= C , X^=-X- , X^+ ^/~ *-K >X

X- 'X -=X . . , X/TZ= 2 m~'

r = 4-

cjieaywiueft neMMbi KoimpyeT aoxasaTenbCTBO npenno-*)2 H3 § 3 pa6oTbi C133

/IEMMA 2.2. U n a K a > K a o f t a n e M e H T a p u o f t

( j j o p M y n b i / " " B r p y n n e A 7 c y m e c T B y e T K.n.

n o n r p y n n a L , r a K a H ' ^ T O ^ ^ 7 £=.fl . H M e H -

H o:

6) Lj'

B) ̂r) =

5. Ceftnac npncrynHM K paccMOTpenHK) HeKOTOpwx anrppHTMHiecKHX

npo6neM, cBsaaHHbix c rpynnofl M . CymecTBeHHbiM ana Bcex na.ifaHefluiHX

paccMOTpeHHft 3Toro naparpat})a 6yaeT (j)aKT cyiuecTBoaaHHa (CM. dime nem-

My 2.3), ana icaJKfloro aneMGHTa rpynnbi M eaHHCTseHHoroKN)

B BHfle KanoHHHecKoro cnoaa, o6naaaroinero cnenyroinHMH

1) na6o oHo(KaHOHHiecKoe cnoao) HMeex ana Ta , rae T - cno -

BO B oSpaayrornHX t>o,t.,... ,~t Q - cnoso HS & , T H 0 HecoKpaTH -

MM;

2) nn6o OHO ecTi, HecoicpaTHMoe cnoao Buna W; Z1 Vv' ̂ ... Vv^, Z VV^.^_ ,

W / ,W 2 , . . . ,W , - KaHOHHHecKHe cnoaa onacaHHoro B 1) THna, nroSoe__

neMMbi 2. 2. MOJKHO npoaecTH Taxwe, onnpascbHa noKaobiBaewyKD HH>Ke neMMy 2.3.

B 3TOM nyHKTe paccy>KaeHHs cneayiox pa6oTe C8H .

18 M.K.Ba/iHeB

us t, (S=1. Z.....K) - oana HS 6yKB d vans. £,••„ (&= — /) , npnneM BW -5 ynonneHbi ycnoBHa:

a) ecnH Z, — t,- •„ (& =±/) , TO nocnenHaa 6yKBa cnosa Wc OT-i» C/̂ ~*.—I J s4

nHHHa or £„,£,, H OT npOHasonbHOH 6yKBbi rpynnbi u ;At /t

6) ecnH £ _ = d , TO Ws ae oicaHHHBaeTca SyKBoii HS ^? ' ;

B) ecna Z" = £/ f TO jm6o W, He OKaHiHBaerca 6yKBOft HS & ,

^ HM66T BHfl Uc,1^,^ ( HJIH if^Crn ) , Tae 6̂ 5 HG OKaHHHBaeTCS

,̂ (cOOTBeTCTB6HHO 6yKBOH C ).

/IEMMA 2.3. J l r o S o f t s n e M e H T n a A / n p e a -

C T 8 B H M e n H H C T B e H H b I M K a H O H H H 6 C K H M

c n o B O M o n n c a H H o r o s w u i e a n n a .

flOKASATE/lbCTBO. CymecxBOBaHHe Tanoro npencTaBjieHHH HOHTH

OHeBHflHHM o6paaoM BHxeKaeT H3 onpeflenaromHX cooTHomeHHH. flna Bbinon-

HHMOCTH ycnoBHa 2,B) aaMeTHM TonfaKO, HTO cnpaseanHBO cooTHOiueHHe:

CL^ci —CLmd 'ct.^ (ananorHHHO nna C ̂ ).

nerKO ycMaTpHBaeTca nna npeACTasneHHH Buna Ta .

B caMOM nene, flBa paBHbix cnoBa W. H W- HS C- HMerar paBHbie npo-

6KUHH Ha o6pa3yK>nme to,tf ,... , t^ . OosTOMy ecnn Tia^=Tzaz .ro^=:7"2

Kf},==-<32, H B CHJiy HecoKpaTHMOCTH, Tf coBnanaeT c T ,a coBnaaaeT c a

CornacHO neMMe BPHTTOHB, ecnn cnoso rpynnbi M , conepxcamee

BxojKaeHHfl 6yKB d H ~t , . , paBHO enHHHue, TO OHO non>KHO coaepacaTfaI i

noacnoBO onHoro HS BHaos ( ^ - cnoso B o6paayioiHHX rpynnw C- ) :

*tf..K v tL-

flcHo, HTO KaHOHHHecKoe cnoBO He MOweT coaepwaTfa TaKHx noncnoB.

, npennonoscHM, nanpHMep, HTO W conep*HT noncnoao

UK^^ • âic KaK ^ necoKpaTHMO, TO O HenycTO. C npyron

CTOpoHbi, nepen SyKBoJS £f/K He MO>KeT cToaTb HH 6yKBa t^ H HH

H3 SyKB rpynnbi G , a tf HMeeT BHa Tq . RonynaeM, HTO Ct = / H 7

SyKBOii, OTHKHHOH OT "t^ . TaK KBK 7" HecoKpaTHMO, no-

, HTO ff ^ \C-t iK\ Paa6op ocTanbHbix cnyiaeB aHanorHnen.

HenocpencTBeHHO Ha caenaHHoro aaMenaHHa cnenyeT, HTO HHKaKoe

cnoBo y/ OT o6paayioiiiHX rpynnw & He Mo>KeT 6biTb pasao KaHOHnnec -

Kowy cnoBy W , coaepacameMy axo^neHHe 6yKB d ann Z^/.v . TBKJ

•& W , T3K »C6 K8K H W , H6 COfl6p>KHT BXOJKAeHHft nOflCnOB BHfla

O cnoxcHOCTH npoSjieMbi TO>KflecTBa ana rpynn - 19

a), B), c) .

Tenepb npeanono>KHM, HTO B rpynne M pasHbi asa

cnoBa:

W; Z, W2 Zz . . . W^ ̂ W^, H w, T, W2 r2 . . . W

HM66M:

' w/'w, z, w,T2

TaK Kan 06 a cjioaa 6binH KaHOHHiecKHMH, TO B nonyneHHOM cnose noacno-

BOM oaHoro KB THHOB a), B ) , c) MOJKex 6biTb TOJIBKO cnoso £ W7 iV/f,.

Orcrona cnenyer, HTO /t/='c/ . Tenepb noKajKSM, HTO W /=W / . Flpeanono -

>KHM, HTO Z = cL (ocTanbHbie cjiynaa aaanorHHHbi). HMGBM:

zL,cL (L=o, t,....m-<), 4. (L=o,f,...,-m.i,a^n ,czm\.

flyCTb W, HM66T BHa Tf Ct / , V/7 HM66T BHA Tf O/ . . TaK K3K W^W^ B (j ,

TO npoeKUHH cnosa n Tf Tf Q/ na \.~t ~t /,...,'ÂTT} paBHa eaaHHue. riosTO-

My r = 7" . Ha ycnoBHa 3, B), nanoKeHHoro na BHa KaHOHHHecKoro cno-

sa, oneBHaHWM o6paaoM BbiTeKaeT TaKace paseHCTBo g =• N .

CnpaBeaJiHBocTfa neMMbi 2.3 nerno nonynaeTca Toraa HnayKUHett nop.

6. PemeHHS Bcex Tex anropHTMHHecKHX npo6neM ana rpynnbi M , o

KOTOpwx 6yaeT naTH penb HHKe, ocHOBaHbi Ha npHBeaenmi CJIOB rpynnbi M

K KaHOHHHecKOMy BHay. OanaKo npa npHseaeHHH K KaHOHHHecKOMy BHay cno-

BO MOJK6T CHnbHO yanHHHTbCH ( HanpHMep, KaHOHHHeCKOe CJIOBO, paBHOe CJIO-

/ V /O 2C vBy CL CL , HMeeT BHa Ct CL ); nosTOMy npnxoaHTca npHMeHHTb H6KOTO-

pbift cneuHanbHbiH cnoco6 aanncH cnos (B aanbHefiineM ana KpaTKOCTH ra-

aanncfa 6yneM HaatmaTb KOBOM). Koa W cnosa W nonynaerca H3

W cneayiomHM o6paaoM. IlycTb W HMeeT Bna^s 'j ^..3/ 2. K

£r£ ,--.,$ ~ o6pa3yromHe rpynnw M -HTIH oSpaTHbie K HHM

/ H at: >O (j = 1,2, . . . , K) . O6o3HaiHM aBOHHHyRD aanncb> HHCJia

oc 5es nepBoft ea«Hnubi sepes 5c (HanpHMep, 5 = Of ). Toraa ana

nonyneHHa vV Hy«Ho B cnose W BMecTO Bcex noacnos BHaa ^ J (£. -

oana H3 6yKB O,^,G^ ,t ̂ , &=•—! , L—OJ,..,!m, ) noacraBHTb cnosa J .<£"..

BxojKaeHHe B cnoso W noacnoaa ôT 6yaeM HaawBarfa ^

cnoea W . Ecna CJIOBO W coaepxHT noacnoso BHaa CL d ' CL^, oC ,

TO ana yaoScTBa B aanbHefiiuHx paccyacaeHHsx 6yaeM cHHTaxb, HTO Bxoicae-

HHH CL^, H ailoT cocTaBnaioT oaHy KOMnoneHTy (aHanornHHo ana c ).m. m

20 M.K.BajmeB

6yKBbi £> '. (i 7O) B CJIOBO 6yaeM HasbmaTb Ci -csoSonHbiM npa

ycnoBHH ; 1) ecjin £— i/ , TO yKasaHHoe exo>KaeHne He

B noncnoBO <2-,-oc" u,- , 2) ecnH £ = — / , TO yuaaaHHoe BxowneHHe He-/

BKJlIOHaeTCH B noacjiOBO &.• d/oC . AnajiorHHHO onpenenaeM noHHTHe C -C u

CBo6onHoro BXOJKA6HHH 6yKBbi ti £ (B 3TOM cnyHae Hy>KHO B ycjiOBHH 1) ro-

o noacjioae S/C-oi. , B ycnoBHii 2) - o noncjiOBe C/oC u/ ). Bxo-6 6 <^ C

6yKBbi t) 6yaeM HasbiBaTt, cnesa U. -CBo6oflHbiM, ecjTH OHO He

BXOAHT B noncnoBO Cioo[-&o , H cnpasa CL - cBo6oaHbiM, ecna OHO He

BXOZIHT B noncnoBO aa CLn cC . HHCJIO a - cBo6onHwx Bxo>KaeHHfi 6yxBH £>•

B CJIOBO W 6yaeM oSosHanaTfa sepea y^(c,CC) , HHCJIO C -CBo6oflHbix

BxcmaeHHft nepes W(L,C) . W(0,O.) 6ynex oSosHanaTb o6mee HHCHO/7

d -cBo6onHbix cjiesa H cnpasa Qyica vo . FoBopa o HHcne sxo>KaeHHfl

HCKOTOpOfi SyKBbI _£> B KOfl CJIOB3 W , 6yfleM HMBTb B BHfly HHC/IO BXO-

)Kfl6HHH _^ B CJIOBO VV (B o6o3HaH6HHHX: I W I j ).

HM66T M6CTO CJI6AyK)maH

/1EMMA 2.4. C y m e c T B y e r M a u i H H a T b i o

p H H T a C 6 M K O C T H O H C H T H a J I H S H p y K )

2_m e f i , H e S o n t u i e f t , . n e M | W l . K o x o p a a J i w -

6 o e C J i o B o V V r p y n n w M n e p e p a 6 a T b i a a e r

B K O H K a H O H H n e c K o r o c n o a a , p a B H O r o

W .

flOKA3ATE.nbCTBO. OycTb W HMeer BHH ̂ ^...A^ (rne^J.^ ..... ̂ ~

oSpaayiomHe rpynnbi M HJIH o6paTHbie K HHM). O6o3HanHM nepea W- non-

CJIOBO ̂ ^ . . ̂ . Pa6ora MauiHHbi pa36HBaeTca aa n. MaKTpOTaKTOB .

ff vB reneHHe nepahix C MaxpoTpaKraTOB nponcxonHT nojryieHHe xonaW^ KBHO-V" j v

HHHecKoro cnoBa, paBHoro cJiosyK^. OSosnaHHM CJIOBO Vê-/ £> /> nepea W^ .

OflHoapeMeHHO c onncaHH6M pa6oTbi MauiHHbi KHnyKUMefi no C noKa>K6MV..

nio6oro npOMewyTOiaoro Me>Kfly Wa u W^ cnoaa l/" cnpaBeanHBOCTb cneny-

romwxA) HHCJIO Bxo>KaeHHH B CJIOBO (S KOMnoneHT 6yKBbi CLO - He 6ojib-

uie,H6M e a e , , ,

6oJibuie,HeM I W ^ I Îw,,! -W*~(C,a) , KOMnoneHT 6yjcBbi C- - HeL °i, ^

6onbme,HeM I W „ I . •+- \Vf.\ — W* f t C) , KOMnoneHT 6yKBbi ± . - Hec UL c °u L

6ojifaiue,HeM I Wgl =6" •

B) HHCJIO BxowaeHHfl jiioSott HS 6yKB CL . C-(/<.rnJ& CJIOBO O - HeP2(rn-i) L L ,

oojrbiiie,HeM C , HHCHO Bxo«0eHHH 6yKBw t • - He Sonbiiie. IBM

O CJIOHCHOCXH npo6neMt>i xojKAecxfia nnfl rpynn 21

C) HUCJIO HH66X, SaHHTblX XOMHOHeHTaMH 6yKB (Zrn , BXOflHfflHX B tff

He •• "m f- u • <- "rn

iti - He Sojibiue, H6M Iv/^l^ (IW^.^ . ,, • • rV '^"Y'rf ' "T "̂

Ha yTsepjKneHHa A) Buxexaex, HTO HHCJIO KOMnoneHT acex 6yKB, KO-

xopoe Morno noaBHXbca Ha nenre, ne 6onee neM 31 W I ; H3 yTBep>KfleHHa

B) BbiTexaeT, HTO nroSaa KOMnoneHxa 6yKB CL; , C;,~t; (i-^rn.) , noas -L< ' c< t-

naiomaaca B npouecce paSoTH, iiMeex .flnnny ne 6onee HSM 2m.LOQ 1WI ;

Ha yTBepwaeHHa C) BbixeKaex, HTO HHcno aneex, aanaTbix

6yKBbi CL i He 6onbiue,HeM

lwl f f +\y/\ - I wi^t- lwl^ - ( I w l ^ - H w l ^ ) <.

• (1Wlc

ana C^ ) . Kpowe xoro, HS onucaHHa anropHTMa 6ynex SCHO,

HTO B nponecce pa6orw HHCHO axo»cneHHft Syna ~U-cl ~b;:,, ne sospa-, ' 'cxaer. OKOHHarejibHO nonyiHM, HTO MaxcHManBHoe HHCJIO aneex, acnontay-

eMbix BO speMfl paSoTbi, He Qonbuie. neM -~- + 6mtiff^ Iwl ~^~ 3l\Vl i T- e-

ana nocTaToiHo 6onbiiiHx i W l CHrHannaHpyioinaa MauiHHbi MeHbme,

IlepexoaHM K onncaHHK) paSoTbi MauiHHbi H K aoKasaxejibCTBy yxsep -

A), B), C). BasHc HHziyKHHH oneBnaeH. PaccMOTpHM •& -ft Maicpo-

paSoTbi MauiHHbi. I1epe6epeM ace BOSMOJKHOCTH ana &g .

cnynafl £.=•*-/( cnynaft t—-1 ,£

Bnonne aHanorHHen) . AnropaTM pa6oxbi B STOM cnyiae saitniOHaeTca B

6yKBH t>; K Hanany cnosa W« AO rex nop, noxa STOLI tz~ iBO3MO»Ho; npH 3TOM Hcnonb3yroTca cooTHouieHHa: ( 1) r7^-^='t^/7 . ̂ ne n

;iH6o 6yKBa Or (j^L, L= — f) , nn6o KOMnoaeHTa oanott na GyxBCt- KUI

&0 OQ &-Q, &~—1 ) H OflHOBpeMeHHO npOBOHaTCa BOSMOKHbie

H o6beaHHeHns cocenHHx KOMnoneHT onnofl H TOH >KG 6yKBbi.

(CoKpameHHa H o6teaHHeHHa xoMnoHenx, o Koxopbix roBopiuiocb BH-

uie, HBJiaioxca cocxaBHofi nacxbio anropnxMOB BO scex paccMaxpHBaewbix

HHxce cjiynaax, H , BO HaSexcaHiie noBxopeHHH, npn onncaHnn STHX anropnx-

MOB OHH ynoMHHaTbca He 6ynyT) .

Tlerxo BHflexb, HTO B onHcanHOM npouecce xa>Kaoe noaaneHne Hosoit

6yxBbi CL- yMGHbiiiaex HHcno Ci -cBo6oaHwx 6yKB $• nac u

22 M.K.Bannes

H, o6paTHO, noasneHHe HOBOfi Ct -cBo6oaHofi SyKBbi u^ Mox.er

Bbi3BaHO TonfaKO coKpauieHHeM CL; -KOMnoHeHTbl, KOTOpaa CBaawBana COOT-Ls

aeTCTByromee sxo>KAeHne SyxBH c7/ (aHanomiHO ana C- ). Kpovie roro,

, HTO HHCJIO KOMnoHeHT SyKBH ~t^ yBejiHHHnocb ne 6onee

Ha 1. Oxcrona Bbirexaer cnpaBejjnHBocTb yTBepscneHHa A). CnpasennHBOCTfa

yrBepjKaeHHa B) BbixeKaer HS xoro, HTO npH npoBeneHHH yKaaaHHoro npo—

uecca HHCJIO BxoscneHHfi SyKBbi CL; (6yKBbi C,- ) yBenKHHnocfa He 6onee IBMO L/

H a l W ^ I ^ . (ana G-o He Sonee HBM Ha 2|V\^-|^ ), r.e. o6mee HHCJIQ BXO» -

6yKBH CL- - He 6onbiue HSM (C — f) rn ° 4- 2.0.^ & . 4HcnoL-

SyKBfai 6- Boo6me He yBenHHHBaerca. HaKOHeii, yTBep^KAeHHe C)LI

H3 Toro, HTO HHcno HieeK, aanaTbix KOMnoHeHTaMH Kaxaoit HS

6yKB ^2/T7 , C/rz , Boofime He ysejitiHHBaeTca, xorfla ^ = Z^/ (.L^=-mJ , H

ne 6onee HGM na I Wg I ^ • xoraa £,„ = Z^/rl .

2) -£„ == Oi . AnropHTM pa6oTw aaKnroiaeTca B npOABHjKeHHH 6yK—

BH cL K nanany cnoBa, npa STOM HcnonfasyroTca coorHouieHHa: (1) nct=dl7,

rae T7 - nH6o oana HS 6yKB Q- (£,——/, L=£m — f ) , nH6o KOMnoneHra

cnpaBennHBOCTH yTBepscfleHHH A) H B) HHISM ne OT-

OT coorseTCTByioinHx noKasaTenbCTB B cnyiae 1). yTBep»cneHae

C) BbrrexaeT HS TOPO, HTO npH npoxoKfleHHH 6yKBM d njiHHa Kascnoft KOM-

6yKB CLrrL,Crn yBenaiHEaeTca Ha enHHHuy, a HHCJIO KOMnoneHT

/T , no npeAnono«6HHK> HHnyKUHH, He Sojiee

IV/Î^ H- I W£ I ,5 CHS 6onee HBM 'W^l^ +'^l/ )•

3) 5» = C^~* . B 3TOM cjiynae nponBHJKeHHe 6yxBbi c£ K Hanany

CJioaa ocymecTBnaeTca B COOTBeTCTBHH c cooTHo-ineHHaMH: (1)^<2^ —Ct,nt

rae /? - jiH6o 6yKsa u- (t^=—'i, Uf'fn—i), jin6o KOMnoneHra oflHofi H3

oc +- / (JU - oana aa 6yKB ̂ H^).

floxasaTenbCTBO nro6oro us yTBep>meHHft A ) , B) H C) coBepmeHHo

OHBBHflHO.

4)^==Zy-Af Cfc= = i / j . PaccMorpHM noapo6HO cnynafi: £=+/ . Pa-

6oTa npoHCxonHT cnenyioinHM oSpaaOM: 6yKBa ^/^ npOABHraeTca K Hana-

ny cnoBa, ncnonfasya cooTHOineHHa: (l)/?£.. ~tf- 17, rae n - nH6o 6yxBac (. (JK y< c t

a 6yKB GL

O CJIOHCHOCTH npo6neMbi ixmnecTBa ana rpynn 23

, tK ; (2) 4-

(anecfa HcnonfaaoBano TO, HTO ~t H C- KOMMyTHpyror); npn STOM BHOBB, J

noHBjiaiomnecH KOMnoneHTbi 6yKBW ~C^ no Mepe noasjieHHfl nponBnraK>Tca K

naqany cnosa scjien sa SyKBofi ~t • • „ , Hcnojibaya cooTBercTByiomHM 06 -it /

paaoM MonH(J)HUHpoBaHHbie cooTHomeHHs HS 1). yTBepacneHHe C) B

cnynae rpHBHanbHO (nanoMHHM, HTO <^,j^.m ). yrBepKfleHHe A) B TOH

n, KOTOpaa KacaercH CL -KOMnoneHT H C -KOMnoneHT,

B 1) paccy»neHH6M, a HHCJTO ~OK -KOMnoHBHT

He 6onee HSM Ha ejiHHHiiy.

FIoKaKeM cnpaseflnHBOCTb yTBep*aeHHa B). flna 6yKB, ornnnHbix or

CLK,CK , L K , noKaaaxenfaCTBo oieaHflno. KaK BHJIHO na cooTHoineHHft ,

HHcno BHOBb noaBHBaHxca Bxo^neHHJi 6yKBbi ~t He Sonfaiue HHCJia Bxowae-v *

HUH 6yKBw C: B cnoao W />_. . KOTOpoe, B CBOK> onepeab, no npeanono -•I K ,f i}2^-/)< rs H#**-*;-//«

>K6HHJO HHZiyKUHH, H6 OOHbllie H6M (C — 1} •$ (C-— f) ( HanO-

MHHM, HTO x < I ). Orcrona HHCJIO Bcex BxoscneHHft 6yKBw ~t^ B nio6oe HS

Mexay W£ H We CJIOB He 6onbiue

H3 BHOBb noaBHBUiHxca BxowaeHHJi SyKBbi ~t K , npoxoaa nepes 6y-

&»• > nopojKnae-T no onnoft 6y-KBe ci., H C^ • HHCJIO BHOBB noaBHB -" K ,

uiHxca npn 9TOM 6yKB CLK ne 6onbUie IBM (£—1) •* . OTCIO -

fla HHCJIO BC6X BXO)KfleHHH SyKBbI O. H6 Sojlbllie H6M ( £, — l) 4-

nna C K ) .

5) _5e - npoasBonbHaa Syjcaa rpynnbi £r . B STOM cnynae sea pa-y,

6oTa COCTOHT B nojiyieHHH Kona cjioaa VVg H cnpaBenniiBOCTb yTBep>Kzie -

HHft A) , B) H C) npoBepaercH TpHBHanbHO.

/leMMa 2.4. aoxaaaHa.

7. Ha JIGMMH 2.4 BbireKaex BaacHoe ana aanbHeftiiiero

nPEflAOÊHHE 3 . C e M K o c T H o f t c H r H a n H a n -2_

p y r o m e f t l v v l p a a p e u i H M u K a w a a H n a c n e -

n y r o i H H x n p o 6 n e M a n a r p y n n H A/ : l ) n p o -

6 n e M a T o a c n e c T B a , 2 ) n p o 6 j i e M a B x o M t a e -

24 M.K.BajiHes

C = J- xH H H B n o n r p y n n bi A . , A . . IQ^ //< m), A.. L ..

6 ;/ -̂ 6/^C ' 6/A

/£>< K< 6</ '< 7-n_; *i .'

flOKASATEJIbCTBO. yrBepscneHHa 1) H 2) HenocpeacTBeHHO

H3 neMM 2.3 H 2.4. fleftcTBHxenfaHo, TBK KaK KaHOHHiecKoe npea -

cnoa ezmHCTBeHHO, TO a) we^ Torna H TOJIWCO Torna, Kornav .

KaHOHHiecKoe CJIOBO (cnenoBarenbHo, H Ron W KaHommecKoro enema)

W HS conepJKHT HH OAaofi HS 6yKB ~t , d H ^/ •„ > H B) W= / xornaV V

H TOJIHKO Torna, Korna W - nycroe cnoao. Ka*floe HS STHX ycnoanft npo-

Bepaercfl

FlepeftneM K noKaaarenfaCTBy yxBep>KneHHa 3).CHaiajia aaMerHM cne-

nyiomee: nycrfa n - necoicpaTHMoe cnoso B o6pa3yK)mnx rpynnw (j ,

CJIOBa • • - ' H e coflep ~Bxo>KfleHHft SyKBbi <§ . Toraa we/? a TOM H TonfaKO B TOM cnyiae,

Koraa BbinojineHO Kaacnoe HS

a) n HMeeT BHfl u. ' (l, &) ,,, ana HeKOTOporo < XQ, x/f ...,* ^ *0 ' * / • • • • • x/-n ̂

6) ana Kascnoro i , me 2 •£•£•£• K , cymecTByeT

'

nycTfa BbinonaeHw ycnoBHa a), 6) H B), Torna

\\, Ha npencTaBneHHa (1) oieaHnHtiM o6paaoM BbixeKaKix ycnosna

a), 6) H B).

JlerKO BHnerb, HTO npencraBjieHHe (1) HecoKparHMO B

c, Tax Kax coKpaTKMOGTi o6pa3yioimix a

i+(H-f)H-f) d+f) <t-H) oaHanana 6w, HTO B Of coKpamawrca BXO-ff-'^-i V/'-l' X'TJ ^g< n o ' . UosTOMy, TaK KaK HecoxpaTHMoe npeacTaaneHHe

B ofipasyroiuHx a ana aneMSHTOB nonrpynnw /7 SHHHCT -< îX^,. ..,Xrr7>

B0HHO, nonynaeM, HTOO6/7 , rae /""" - HSKOTOpaa (fiopMyna, Toraa H

TOJibxo Toraa, Koraa nio6oft HS seKTopoa < x^ , xy , . . . , Xm > , ynacT-

B ycnoBuax a) , 6) K B ) , npHnannewHT MHoacecTBy HCTHHHOCTH

O CJIOWHOCTH npoSjieMbi TQMtAecTsa ana rpynn _ 25

. AjiropHTM npoeepKH npHHanne^nocTH BeKTOpa K MHoacecTBy

HCTHHHOCTH sjieMeHTapHOH 4>opMyjibi oneBHAeH H He Tpe6yer AonojiHHTejifa -

Hbix HHeeK npH peajiHsauHH Ha MauiHHe TfaiopHHra. Kpowe Toro,

HTO npoeepKa BbinojiHeHHfl Kawnoro HS ycnoBHfi a), 6) H B) T&KXG

SbiTfa BbmojiHena Ha MauiHHe TbiopHHra Sea npHBJieieHna nonojimrrejifaHbix

aneeic, TBK KaK Kaixaoe us CJIOB u d) dj (£) HMeeT flJinHy, He

\+- ...+\O . \ I CL\ TaKHM o6pa3OM, nonyiaeM, HTO

npnnaane>KHOcTfa cjiosa g, HS Q- K nio6oH us nonrpynn fl- ,/-!••i (t L LJ

* £ pac-

nO3Hana na MauiHne TbiopHHra c CHrHannsHpyromeft \o \ OneBHflHO, HTO

3TO HM66T M6CTO H B TOM CJiyHae, KOPfla BM6CTO Q paCCMaTpHBa6TCH/

ero Kon.

OKOHiaTenbHo cnpaaeanHBOCTb yTBepJKneHHs 3) BbiTexaex HS JIGMMH

2.4 H cneayjouiHx nerKO npoBepaeMwx yTBepxflSHHJi, ycTaHaBnuBaromax BHA

KanoHHiecKHx cnos ana sneMenroB nio6oH HS noarpynn, o KOTOpux HAST

pent B yxBepjKaeHHH 3) npeAnoweHHa 3:

(1) ecnH w e / y . . TO KaHOHHnecKoe CJIOBO VV . paBHoe W ,yC

eT BHA TQ , rAe 7~ - CJIOBO B o6pa3yiofflnx ti~ CZ-7^6j, Q€-fl; ',7 _ Zs if L(2) ecnH vv e L~- , TO \ HMeeT BHA J '<y , TAB 7" - CJIOBO B 06-

paayiofflHx t; t: H t-(t=^L,i} , qefl~^: \ j ,7, J ___ ./ CJ

(3) ecjin w £ L ,- •„ , TO w HMGGT BHA To. , rAe 7" - CJIOBOJ . . " •*•

B o6pa3yroranx t^t^ , t:tK H tz (1i=L,j,K') , O.G fl ' ̂ K ;^j t __ ̂ * J _^

(4) ecnH W6 LJ::K < TO W HMeeT BHA To , rue J~ - CJIOBO B

*

(5) ecnH we texp , TO W HMeeT BHA 7 ,̂ /^ - - - T^fr TK ,

-L (L O,t,,..,

T; 7^= / , 6CJIH iu

npenno»;eHHe 3

9. BseaeM HeKOTopwe oSosHaneHHH: TJ ,/< SyAeT o6o3HaHaTt CJIOBO

- nonrpymiy

n.&m , C,^ \y nnbi M in B -noarpynny

.

KpOMe TOPO, sesae B aajibneiliiieM BMecro 6yKB CLQ , VQ , £- 6yaeM/7 . .

CL,f},t- . CyMMy cTenenefi Bxo^KAeHHH SyKBbi S B CJIOBO W 6yoeM na —

aecoM ^ B W H oSosHanaTfa nepes

cueayiomyio neMMy.

26 M.K.BanHeB

/1EMMA 2.5. n y c T b W - c n o B O B o 5 p a 3 y 10

I U H X r p y n n b i AY . T o r A a e c n n W& B> , T O

AOKASATE/lbCTBO. FlycTb W oSoaHanaeT KaHOHnnecKoe cnOBo,'-̂ /-v f~*~'

paBHOe yV . Tax KaK W€ G , TO W - CJIOBO rpynnw G . ECJIH W

He coaep>KHT BXO*neHHft 6yKB CL,o , TO W€ B . OosTOMy MO>«eM CHH-

TBTfa, HTO W HM66T BHfl (/ U & . . . U ti

Ba B o6pa3yroinHx a , O , oTnHHHbie OT

B o6pa3yiOfflHX CL/,£l,Cf,...,O-rri,6rTl,C ,

! ̂ t

npnHaone>KHT noarpynne E> — \Q..,L—O,'t-1,—2...\

it f , Ci£ , . . . , U. ̂ -

O , ..., (J^ - CJIOBB

(f.^-l, ecna : =£= O ,

Torna H Tonbxo Torna, Korna nK>6oe us

cnynae,

-.-

- S , OHO coflep>KHT xoTS 6w OQHO BXOKfleHHe SyKBw $ . B npo-

aecce npnaeneHHa en OB a W K KaHOHKnecKOMy BHny HeKoropwe axowae -

HHH SyKBbi u MoryT coKpaTHTbca, a HOBUX Bxo>KneHnfl arofi 6yKBw He

OTMBTHM B W Te Bxo>KfleHHa 6yKBH -Q , KOTOpwe coxpanaiOTca B

Bcero aroro npouecca H, cneaoBaxenBHo, BXOBHT TBKJKe H B W .O if f £/j / ̂ K

3TO Dynyr Bxo%aeHHa v , u , . . . , O . Torna cnoso W

a cnoBo W HMeeT BHA:

£y "»̂ J> I

W/ . . . 6

O6o3HaiHM nepea oc^ Bee 6yKBbi'***' & 'noe cnoBo \v- HMeex na6o

v —<X • + OC/ = <X/

it U CHe

PaccMOTpHM HeKOTOpoe cnoBo

HM66T BHA

B cnoBe w- • HCHO, HTO KBJK-of OC~'

L *• O~ CL L

ct,

, HCXOAH us BbiiuecKaaaHaoro, OHO

Ha ycnoBHa u • & E> nerno nonyiaeM, HTO Bee (U--)a 6yKBH CL B cno-

u.- paaeH aynio, T.e.

H,

O cnojKHOCTH npoSneMbi TOwnecTBa ana rpynn 27

ft-^+i £c* ,^- - _ O' — _ . . # _ _ _ _ _ • (2)

KpOMe Toro,

(U- ) "+" (U-7) +

OTCJOH&

Ha (2) H (3) cnenyex, HTO nio6oe aa £/. , a cjieflOBarenfaHO, u y/rj W •/

noarpynne o , rae

f, HTO

(4)

OUBHHM cHanana Kaacnoe HSOC- B OTAejitnocTH. PaccMOTpHM cnynaft:L/

< L < K . ripocneaHM sa HSMeneHHeM seca 6yKBbi Q. MeKny BXO -

o ' H a ^+/ B npouecce nonyneHHH W HS W .

HTO BbinonneHHe coKpameHHJi H npeo6pa3OBaHHK cornacHo cooTHomenHaM,

KOTOpwe nn6o He conepwar 6yKBbi & » nn6o yKaawBaioT aa KOMMyTHpo -

BaHHe HeKOTOpoft 6yKBbi c CL , ae MBHSHOT Beca 6yKBbi CL B nio6oM nofl-

cnose. HosTOMy ocraeTca paccMOTpeTfa BbinonneHHe npeoSpaaOBaHHfi Buna:

e ̂ , 4> 1 09 —O, / O, O, .K 5 i .= 2 2 ' ^ =

3aM6THM, HTO ecjiH npeo6pa3OBaHne yKaaaHHoro THna KacaeTca BXO>K-

6yKBbi O , oTjinnHoro OT exoacaeHHft o u H V ^' , TO

Beca SyKBH CL B noacnoBe, aaicnioHeHHOM Me>Koy Bxo>KaeHHHMH -o C H D

He nponcxonHT. Ka%aaa SyKBa ~t/ , npoxona nepea 6 6 , nopoxc-

cnpasa OT Hee SyKBy CL , H, npoxonn nepea u ^ ' , nopoHcnaeT cne-c ,

OT Hee 6yKBy CL . UosTOMy, nonciHTbiBaa oomafi Bee oyKB ij , KO-

Topue npoxonaT nepea D 6 H O ^' , MOWOM ouenurb o6mHii npnpocT y.

seca 6yKBbi CL Me>Kay 6yK&aMn f> ' a o c'"l"/. B npouecce nojiyneHHa

W us W nepea 6yKBy ^ ^ npoxonaT see 6yKBbi ~b , KOTopwe

BxonaT B \ npasee, HBM -g L , nepea v c ' npoxoasrr 6yKBw ^ ,

KOTopwe BxonaT B W npasee, IBM V c ' . KpoMe xoro, HOBUX sxo»cfle-

HHft 6yKBbi t B TeqeHHe scero npouecca He noaBjiaeTca. OTcroaa nemo

28 M.K.BamaeB

, HTO y . = f

Ke oSpasoM

: «:,*= I oC_ -1- of. -*-...+ oc • I .L u I L

nna nio6oro L , HTO

6) |. (W/V + (

Bee 6yKBW CJL B W pasen nynio, T.e. (W^^^ (W; }

a)

6) aoKaatiBaeTCH anajiorHHHo, Hcnonbayn TO, HTO sec

6yKBbi "t B W paseH•x-

Ha (5) H yTBep»neHHii a), 6) nonyiaeM, HTO (X^- -

TaK KaK B \ HMeeTca XOTH 6bi OZIHO BXO>KfleHne SyKBw ~u , nonynaeM,

HTO

* / f'W' "'-I f * - n, , . [ IW| - / 1OC • 4s 2 > oc = rn_cLOC, \&.; , L—u,f,.. .,X] -4= £

HepaBeHCTBO (4) aOKaaano, H BMecTe c STUM aaaepiiiaeTCfl floxaaa-

eMMbi 2.5.

10. riycTfa S ~ HeKOTOpoe MHOJKB CTBO HaTypanfaHwx HHCGJI. O6oaHa-

HepeSigg noflrpynny | {>^ , Le. S,at, V1tC^ ... .,CLm. &m ,Crn]

nbi M . Ha neMMbi 2.5 BbiTescaeT saKHoe nna nocnenyromero

OPEfl/lO>KEHHE 4. F I p o 6 n e M a E x o x a e H H a

c n o B a y / H 3 r p y n n b i A f B n o a r p y n n y ^^

p e i u a e T C H H a M a u i H H e c S - o p a x y n o M

"BuXxBdo- gf or«nnowou o qj.H3OHej.oA OHSKOW \<~)'3'1 ' Q\n x 'TI ixooHwairDBHHdu fa -x ' 5 9(-x>-"'— 'p— 3O_ ) anaouoX OHaHuouna

(f—C/ÎÔ)] oaogoiu BUD BDJOX 'BDJOX oxûox H BEJOX (5 99' '• Q} 9

3-77 OXH 'waBHXuoii BDcsoxQ • (9) xo WHHHHUXO '• weHHsuaBxoDsdii â/• *

XHinoiXeBdgo a WHJNHXBdxooaH WHaXdD qxBDBugo XSMCOFM SH -77

j "' '3+ '/^'^=7 9 f ^nnâuoii HWHmcuXeBdgo Hwwmrogoao

• • '?'<2 XHinoiXeBdgo a ownxedsooeH aHHsi/aBxonedu oxe

J.8JKOW

etTHS a OHBOHUBBr -j r

"77 OXh 'WSBhÛOU OSJ8U Q~ P +" ' -f- 'x" -f°X> zs77̂ 77 j BaXOH83Bd

sod

- OXOX8H ixoXn Xwoieoy • <7;9M ox ' Q raaxXg gHHetrxoxa xHwdstroo 8H/" t o

• • ' ^•77 oaouo OHWO rag BXOX Hirog • J S ^ ? ' ^ 9\u-iWJtfoii

•77 aoiro EH eoDMCBx BUJOX 'Btruox oaiuox H Btraox ?3M oxh 'OHOB 'oaox

' j - ^7 7 \u XHweimBHHdii -77 oaoifD /"

oaogom Him OXH 'xaXuai/o g'g rmwau en BDJOX ' 0 3 M 'oH«=tif8XBaoP8iw

/ xeoa BUIT OXH '«W,BXHHO watr/Cg

ox ' -77 eaoifo oaontro BITD rag BXOX £7 ^7~'(-71) Huog 'xeehe XNH

* «JirexHHi;oiioD BHHeheifaHdu eeg BHeHUouna qxng XO>KOW Bxdeaodii BXS OXH

'OHtTHasHo ' '77 a Z7 raaxXg Boea rauXH BaxoneaBd enaoirojC -77 aoiro xeoa

BUD BoxsBdsaodu BUBHBHD sshjCuo woxe g • -2 ^t / ' Q^f HUOS ' / =^ -/2

JMSHHdu ' ^LJ0'iiJO.'lJ~'v''"''y''Q''7^ xHinoiXeBdgo a aoiro xwdoxossH ntrox

- 2/7'"'*!/7'^7 Baoiro J Q. '73 xHincuXcedgo a 2'77""'777 ''r> aouo xiqdoxoxen

wDox - Z77'' " ' *7l''n 8Da "2V7277"'^?/77'3Y7 DHa XSSWH A\x— — — -- -- _ A

qxadxowooed BOXSBXOO 'oHiuexBaoDeifQ g73M ox ' a '^7 axXg

8H H j EH BaOIfO BOX - /A HUOg ' £ 7 M 'OH<?LfeXBaon8UO 'H

ox ' • y' p' J- a^^g BHHSDxoxa xnwdeDoo M Hi/og •( xeshs |/V\A t

wsh sauog an BoieXeHiroiiOH woxe ndii '^'g SWIMSLT OHOBiraoo) M oaonaBd

' Baouo oaoxoaHHHOHBX /v\x a BoxaBaiqxBgBdedaii M BITBHBHQ -woeA

-Bdgo jMHmcuXDsuo XHKBUjiqa BHHsDaao ooanodu '

- 1 U O g G H X B U O K H

o ' |M| j j e m o i X d HC

UUjCdj BUD B3XO8D3KOX KWel/gOdll HXOOH5KOI/O

30 M.K.BajmeB

K HeMy c BonpocaMH o npHHan.ne>KHocTH K S nna scex incen:

Ilpn sroM H3 ycnoBHH U-& {~6 - . ,64 —-p— BbiTeKaex, HTO nK>6oe

o KoropOM saflaerca Bonpoc opaKyny, He MOMST 6biTb> 6onfaiiie HOM - — .

3AMEHAHME. Kax BHHHO us noKasaxejifaCTBa npeanoxeHHa 4, ecnH

cnoBO vv us rpynnbi M ne conepjKHT Bxo>KneHntt 6yKBH ft , TO nna He-

ro npoSneMa Bxo>KfleHH« B B pemaexca na o6biHHoii MauiHHe TfaiopHara c

Iwl •

§ 3. noctpoeHne rpynnu /Vc H

1 H 2

1. FIpHCTynHM K OKOHHarenbHOMy nocxpoeHHro rpynnbi W, . Ho xoay

nocrpoeHHa cpasy ace 6yflyx paccMarpHBaTfaCH HeKoropbie anropHTMHnec -

KH6 BOnpOCbl.

OSosHaHHM nepes M rpynny, H3OMOp4>Hyio rpynne M npn HSOMOP -

: a—*-a(L>t aeM .

ITycTb B npencraBjieHHe MHOxecrsa S

BxoaflT aneweHTapHbie (xapMyjibi , 2 , . . . , „ •

IlocTpoHM HeKOTopyM rpynny A^ cnenyioinHM o6paaoM: o6pasyeM

GBo6onHoe npon3BeneHHe W" rpynn M H A/ c o6-beaHHeHHeM noa -

rpynn G K G > nanee 6epeM CBoSoanoe npOHSBeaemie J^f nojiyieHHoftir(°> i J l f e ) * i O I (*)rpynnbi M H rpynnw M c oSieanHeHHeM noarpynn L, H /_, H rax

.. ir(P~')' *-oanee, Konnaa CBOoonHWM npoH3BeaeHHeM rpynnw J\ rpynnw

c oS-beaHHeHHeM nonrpynn /. w.Lt, (Beaae o6i,enHHeHne nonrpynn

npOHCXOflHT B COOTB6TCTBHH C TpHBHanfaHbIM H3OMOp<J)H3MOM: CL — «-

2. HMeer M6CTO cnenyiooiafl

tf(P} - K.O

B r p y n n e W B b i n o j i H e H O p a -

HEMMA 3.1. a) tf(P} - K.O. r p y n n a; 6)

B e H c T B o:WU*-

flOKASATE/IbCTBO. XTBep>KfleHHe a) OHSBHAHO, T.K. see

O cnojKHOCTH npo6neMH TOjKAecTBa ana rpynn 31

nonrpynnbi smjiawrca KOHSHHO nopo>KAeHHbiMH. yxBepjKneHHe 6) BW-

H3 HSBeCTHblX CBOftCTB CBo6oaHbIX npOH3BeA6HH8 C oSteflHHeHHOfi

noArpynnoft. floKa*eM yTBepjKASHHe B) . Hcno/ibaya HasecTHbie cBoftcTBa

CBo6onnbix npoHSBeaeHHft c o6iennH6HHoft nonrpynnoft, KnayK.uw.eii no D

HTO

= fl _ n ft n . . n fl .i z. p ri rt ' p

CnoBa d cBoSoAHo nopoKAaior B M nonrpynny>

Y XL=0,+i.±2,... ,1=0,1. ...,n\ '" ' ' rn

Orcrona oneBHAHbiM o6pasoM nonyiaeivi, HTO /7_ ft /?_ r~l...fifl- = /?ri rz i 7

YrBep>KfleHHe B)

onao oSoaHaieirae (CM. C 6 3 ) . riycrfa /7. H /7 - noarpyn-

nw HeKoropoB rpynnbi %/ . Torna nepea /7 . /? SyneM oSosHanaTfa MHO-

cnoB rpynnw ¥f , paBHbix B ̂ cnoeaM BHaa U.V

/1EMMA 3.2. a ) I l p o S n e M a T O « A e c T B a A J I Bis(P>r p y n n b i ^ V p a a p e n i H M a n a M a in H H e T f a i o -

p H H r* a c e M K O C T H O H c u r ^ H a j i H a u p y 10 TTT Q H2

Iv / l 5 6 ) c H / i f a H b i e n p o 6 n e M b i B x o a c A e H H a

a a p e i i i H M b i c C H r H a n a s H -

p y K) m e ft I w l . n p H i e M A n n H a n o n y n e H H o r o

c n o B a H e S o n t m e i e' M I w l .

flOKASATE/lbCTBO npoaeASM no HHAyKUHH. 1) FIoKa^KeM cnpaBeA -

neMMbi ana rpynnw TV . Corjiacno neMMe 1.5 npuBeneHHe K

HopManfaHoft (jjopMe CJIOB rpynnw JV" MOXBT SwTfa ocymecTBJieHO 6ea pac -

na MauiHHe T ,, c opaicynoM, pemaioinHM npo6neMy BxowfleHHa B

noarpynny G Ana cnoa HS M . CornacHO npea;io>KeHHio 3, STOT opaxyn

6biTfa saMeHeH o6wHHOft MauiHHOft T c cHrHanHSHpyioinefi I Wl . Cy-

nepnoaHiiHfl MauiHH 7"_, H T aaeT oSbiHHyro MauiHHy TfaiopHHra c cnrnanH -2 r^J

3Hpyiomefi|wl , Koxopaa npHBOflHT nro6oe CIIOBO W rpynnw W K Hop-,j jf.

ij)opMe W Buna Vv^ W . . W^. , npanfeM Iw I <• I W I . Cnpa-

yTBepacneHHa a) BbixeKaer rorna HenocpeacTBeHHO HS neMMbi

1.4, Teas. KaK n.r. Ana M H M paapeuiHMH c cnrHanHaHpyionieft iw|

YTBepjKAeHHe 6) BbiresaeT as cnenyiojHHx aaMeiaHnfl, oneBHAHbiM o6pa -

BOM nonyiaeMWx HS neMMH 1.4:

A) y/eM (HJIH W6A7 ) xoraa H xonjbKo rorAa, Korna Z- == / n Wy -

32 M.K.BanHeB

CJTOBO H3 M (cOOTBeTCTB6HHO W7 - CnOBO H3

B) y/e M . M Toraa H TojibKo Toraa, Korna Z^2,W /eA7, vsêA/ ,

2) IlycTfa neMMa cnpaBennuBa AJIH .//" . Hro6bi noKaaaxfa ee cnpa-

ana TV , TBK we, Kan B cnynae 1), nocraTOHHO noxaaaTb,

HTO npHBeneHHe K HopManbHofi 4>opMe cnoBa W H3 .A/" MOJKBT 6biTb npo -

B6A6HO c CHrHanHSHpyroraeft Iw! H HTO fljiHHa HOpManfaHoft ÔPMH W* He

6oni.uie H6M |v/l . Tax KaK yrBepwaeHHa, ananorHHHbie A) H B), B nan -

HOM cnynae xaK>Ke HMBIOT Mecro. OpHBeaeHne W K HopMajifaHOfi 4»pMe

Mower 6wTb ocymecTBJieHo oSbiHHbiM cnoco6oM coKparaeHHH HHcna MHOJKH-

reneft. Una nonyneHHH TpeSyeMbix OUBHOK aaMSTHM ronfaKO nsa cnenyroinHx

: (1) npHHaajieKHOCTfa HeKOTOporo MHOKHTBJIH LL HsvV", (L) ,. K

K nonrpynne U.- Master otiTb nposepeHa cneayiomHM oopaaoM: cnana-is (/' )

Jia ana Li pemaercfl canfaHaa npoSneMa axojKfleHHH B M- (cornacno HH -2

nyKUHOHHOMy npeanono»eHHio, STO HcnonbayeT He Sonee IBM I W l aneeK,

npHieM fljiHHa nonyneHHoro cnosa V~ He 6onbme HBM I w l ^ , nocne sxoro2

yxe ana c/ pemaerca c cHrHanHSHpyromeft I V\a sxo>KfleHHa B/ (£) ,r.l • v^ / (£> , V *J (i> VL , H (2) ecnH (j£ L, , TO (Tax KaK u - CJIOBO HS M ) co-

/* Lt

OTBeTCTByromee CHOBO H3 M Cc ' , paBHoe £/ , nonynaeTca npocTO noa -

CTaHOBKOft B U BM6CTO 6yKB Q C 6yKB Q, , T.6. flrtHHa CflOBa H67 '

yBenHHHBaeTca. JleMMa 3.2 aoxaaana

3. riycTb J^C - rpynna, H3OMOp<J>Haa rpynne TV cornacno

H30Mop<})H3My t ~Q.—*~Ci, CL&ff . Torna rpynny N HOCTPOHM KBKf t * , ~ *»

CBo6oflHoe nponsBeneHHe rpynn N H _f\f c o6i>eaHHeHHeM noarpynn

M in M cornacHO H3OMOp<{>H3My X> , T.e.

KT / A / - r c? L r L.TVg = \N ,N ;k.=h.,rie

Ms neMMbi 1.3 H yTBepacASHHH B) neMMbi 3.1 oqeBHAHbiM o6pasoM

HEMMA 3.3. n o n r p y n n o f i J M , M\n H // a B -

n a e T c a r p y n n a JA7, M, /L=/ t , /Z .G/*7™}.

Una rpynnbi W& cnpaBezuiHBa Taxme cneayH3inaH

71EMMA 3.4. a ) H p o 6 n e M a T O « a e c T B a n n a

r p y n n u Wg p a s p e u i H M a c C H r H a n H a a p y -2.

K> m e ft I W l .

6) C H n b H a a n p o 6 n e M a B x o j K a e H H a Bt "^ i

n o n r p y n n y j / V . M j p a s p e u i H M a c c H r a a n H -

O CJIOJKHOCTH npo6neMbi TojKnecTaa ana rpynn 33

a n p y i o i n e i i Iv / l , n p H H e M A Ji H H a n o j i y n a e -

M O T O c n o a a He 6 o n b in e H e M | \ I .

AOKASATE/IbCTBO. Cnanana aaMeTHM, HTO H3 JICMM 1.5 H 3.2 BH-

TGKaeT, HTO npHseaeHHe cnosa W HS //5 K HopMaJibHofi 4>opMe W^MOHCQT

6biTb npoBeneao c CHPHanHSHpyiomeft |Wl , npHHew ly/*l -4 I Wl . CnpaaeA-

nimocTfa yTsep>KaeHHs a) BbixeicaeT orcroaa, KaK oBbiHHO,. c noMomtro neM-

MH 1.4.

\

AoKa>KeM yxBepjKfleHHe 6). IlycTfa W HMeer BHfl W. W, . . . W^. . By-(P)cHHTarfa, HTO Z-> / a v e W (Koraa -^=/ , aeno cBoflHrca K neM-

f '̂ i3.2 ). IIpeanojiojKHM, HTO we j M, M \ Toraa ana v/ cymecTBy-

er npencTaaneHHe W B HopMantnoft ÔP1^6 Bnna ij t? ...(/ , rae s > / i*~*j

Ka>Kfloe tf; Jie>KHT nn6o B M , JinSo B M H He npHHaflneacHT ff __ MMB-L> VIC

Me

- -TaK nan nro6oe us cnos W H W HMeer HopManfaHyw (ôpMy, TO coxpa -

inenae nacna MHO*HTenefi MOweT SbiTfa TonfaKO B cepeAHHe.

, T.e. \^=C'a , rue '

nepea W 2 . Tax KaKê M H W, ^ M , TO > A/

OTcrona nonynaeM, HTO (7 'w, € M , T.e. V/. = t/i^ H T.O. Ec-

JIH t^-S, TO HGKOTOpoe cnoBo, He npHHannejKamee M , OKaaanocfa

6bi paBHbiM enHHHue, nero He MO«eT 6wTfa. CnenosaTenfaHO, 'L == S u•r—i

V W& = ' . OSpaTHO, ecnH BbinonneHbi ycnoBHa: \ 6 M . M

W-€.M. A7 npn H6THOM i, \\f-£ M . M npa neneTHOM i,. v — '

(i, < t) H W^. npHHannejKHT A/ npa neneTHOM 1 HJIH /W npn H6THOM 1. ,

TO W& {A/, A/ } . TaKHM o6pa30M, HJIS TOTO HToSw peiiiHTb npo6ne\iy

Bxo«neHHa B |A/,M| , aocTaTOHHO npOBeparfa Bee yxasaHHbie ycnoBna.

Ecnn HcnonfaaosaTfa ana nposepKH STHX ycnoBHft MauiHHy TbropHHra, pe -

uiaroiHyio cHnbHyro npoSneMy BxoxneHHa B M, M , cymecTBOBamie KO-

Topoft yTBepjKnaeTca B neMMe 3.2, TO MW MOX.&M rapaHTHposaTb, HTO ana

Kaxcaoro i

I £/.• I + I U,. I < I W.- 1 .U U L/

Hs 3Toro HepaaeHCTBa nerKO no/iynaioTCH cjienyroiHHe HepaaeHCTBa, KOTO-v

pue coBMecTHo c neMMoft 3.2 naK>T Tpe6yeMoe yTBep>KneHHe:

(i> = f,2. ..... ^) 2) \ t f l \2l-f-. ..4-16^14 IWl. HepaaeHCTBo 1) nerxo

nonynaeTCH no HHflyKmiM. flna nonyneHHfl HepaBencTBa 2) aaMexnM, HTO

34 M.K.BarmeB

li/ 'i^- I W / l - M a - I —\U,-\, ( L — 1,2,...,1~) . CicnaabiBaa Bee STH He-6- C 6 — / w

paeeHCTBa, nonynaeM i t/l + 16^1+. . . + I 6^1 < I V/l-HwJ-K . .+ I w.̂ 1 . /IeM-

MB 3.4 noKaaaHa.

4. HanoMHHM, ITO S - p.n. MHO^BCTBO, Hcxona us Koxoporo MW

CTporoiH TVg , H Bs - nonrpynna { a~6Z&Z6, ie.S,a,, &, ,C, ..... C^] rpyn-

nw J\f . O6o3HaqHM nepea Q K.n. nonrpynny | M ,Q./,U/,Cl,...,Q.rn,Drrl,Crr[\u TV" .

B cnenyiomHx flByx nynKrax sroro naparpa(J)a 6yner noKaaano, HTO

rpynntiTv^ H eS nonrpynnbi Q cnpaseflnHBbi npenno>KeHHa 1 H 2 ,

B nyHKre 1 naparpacjm 2. Caaiana noKa>KeM cnpasennH-

3.5. QS={M,B5; =h,flOKA3ATE/Ih>CTBO. a) CHanana noxa>KeM, HTO noarpynna Q B

rpynne TV- nopownaeTca noarpynnaMH M H E> -. fleiicTBHTenfaso, HMGIOT

xoro, BcnoMHHast, HTO fl = \CL , v vfee i <x0,xf,...,

nerxo MOxceM nonyHHTt, HTO

a) aoxaaaHo.

6) Torna neMMa 3.6 nerKO cneayex H3 JIBMM 1.3 H 3.3.

5. floicaxceM npenno>KeHHe 1 : i,e. S Toraa H xonfaKO. Toraa, jtorna

OL Cvd € Q c • ^3 neMMbi 3.5 BbiTeicaeT, HTO Q^HM =5<- i

(D

,-i =

i 2 , . . • [ • -HosTOMy HMeex MecTO

(2)

1 cnenyeT us (1) H (2).

6. AoKa«eM npeajumeHHe 2, T.e. HBM ny»HO noicasaTfa, HTO npo6ne -

Ma Bxoxnemia B noarpynny ^7 ana cnosa W HS rpynnbiTV^ CBOflHTca K

O cnoacHQCTH npoSjieMbi ToatflecxBa ana rpynn _ 35

2npo6neMe paapeiiiHMOCTH ana S c CHrHanHsupyromeH IWI , c aanpoca -

MH o HHCJiax, He SonfaiuHx, HeM I - — — - - | _ CorjiacHO neMMe 3.4, cpa-

sy w;e MOJKBM CHHxaxb, HTO W - cnOBO H3 noArpynnfai I M, M I . HPHBO-s*^

AHM v/ K HopManbHOH (JJOpMe W, W,, . . . W_ , rne W, . , , €. M ,w,-SM.I c . L c.C> I £v

3xo MO5K6T 6biTb cnertaHO Ha oSbiHHoft MamHHe TbropHHra c cHrHann3Hpy -

l\vl . Torna, Hcncwibays neMMy 3.5, paccyKflSHHHMH, aHanorHHHbi -

MH T6M, KOTOpbie npoBefleHbi npH flOKaaarenbCTBe neMMH 3.4, nerxo nony-

HTO \V£ Q Toraa H ronbKo xorna, Korna nroSoe H3 W-. , , npa-

K nonrpynne E> ,. . ripezuio>KeHHe 2 BbireKaer Torna H3 npenno —

JK6HHH 4, rax KaK nro6oe HS W; HMeex annay, He 6ojibinyio,u7. B saRnroneHHe axoro riaparpacfia npHBeaew neKOxopbie

Koropbie 6yoyT HcnojifaSOBaHbi B § 4.

3AME4AHHE 1. Bee onpenejiHioiiine cooTHomeHna rpynnw J\f,.

KOTOpbie BXOaHT 6yKBbI

*n (3)

BHA:

rzie U-1 , U^ , t£s ,U^ ne conepwax 6yKB H3 cnncKa (3), £, , 3Z - 6yKBbi HS

(3). FlepenHCfaiBaa cooTHOiueHHe (4) B

nonynaeM, HTO SyKBy 5 MOKHO BwpaaHTfa nepea ocTanfaHbie QyKBw rpyn-

nbi J*f . /lerKO BHneTfa, HTO ana. Ka>Kaoft QyKBbi ,5 aa (3) HMeeTca ue-

noHKa cooTHomeHHft rpynnw Wfi BHfla (4 ) , Hcnonbaya Koxopwe MO>KHO no -

nynHTb CJIOBO t/t , pasHoe ^ H He coaep>Kainee 6yxB us (3), KPOMS

6yKBH S . (HanpuMep, ana 6yKBbi ^ cooxBeTCTByroniaa uenonKa 6yaex:

Fpynny, nojiyiaeMyio HS N yaaneHHeM oSpaayromHx us (3) KpOMe S ,

H noacxaHOBKoft cnoBa tf* BMBCTO 6yKBbi £> BO scex cooxHOineHHHX, 060 -

3H8HHM Hepes^j. . OSosHaHHM Hepea P - nonrpynny rpynnw i, , o6pa -•" -* ' s ~

ayiomHMM KOTOPOH asnaraxcfl see o6paayK>inHe noarpynnw Q <. , KpoMe o ,

BM6CTO KOTOpoS B KaHecTBe o6pasyioinefl ana P Ao6aBneHO CJIOBO ifff- .

OneBHflHO, HTO npeanojKeHHH 1 H 2 ocTanyTca cnpaseAnHBbiMH, ecnn

B HHX BM6CTO N, nOACTaBHXb /. H BM6CXO Q nOACXaBHXfa Pz> 5 5 S'

3AME4AHHE 2. Bbime npH AOKaaaxenbcxse npeAnoaceHHa 2 6bm yxa-

36

3an anropHTM, Koropbifi cBoaHT npo6neMy Bxo«neHna B noarpynny QL ana

cnosa w" us rpynnti AV K npoSnerne BxowaeHHH B nonrpynny B> _ ana

CJIOB rpynnbi M . ripocne>KHBaa npouecc pa6orbi sxoro anropnTMa, ner-

KO saMerHTfa, HTO nK)6oe npeo6pa3OBaHHe, BbinonHaeivioe B STOM npouecce,

He yaejiHHHBaeT o6mero HHcna sxoxaeHHH 6yKB HS (3) B npeo6pasyeMOM

cnose. Orciofla nonynaeM, HTO, ecna W ne conepîiT 6yKB us (3) , TO

npo6jieMa Bxo^neHna B Q, ana Hero (IWIH, MTO TO «e caMoe, npofinevia

Bxo>KneHna B P ana cnosa HS ^ ^ , He coaepjKamero SyjcBbi ^ ) CBO-

flKTCH K npo6jieM6 BXO>KZieHH9 B E> flJlfl CHOB, H6 COflepKafflHX 6yKBbI V

H, corjiacHO aaMeiaHHio nocne npeAJio>KeHHH 4, pemaeTca na o6biHHOfl Ma-2

c carHajiH3HpyK)inefi IV/ l .

§ 4. SaaepmeHHe aoKaaaTenBCTBa reopeMbi 1

1. Ceftiac noKaaceM, HTO, acxona us rpynnbi A , nna nio6orov

MOJKHO nocTpoHTfa K.o. rpynny /<" , ana KOTOpofi cnpaBeflnHBbi cneayiomHe

2 yTBepxneHHfl.

nPEfl/IOÊHHE 5 . I I p o 6 n e M a p a s p e u i H M O c -

T H a n H p.n. M H O J K e C T B a S C B O f l H T C a K

^ isWn p o 6 n e M e T O * a e c T B a a n a K c C H r n a -

c s a n p o c o M o p a -

B e n c T B e e n H H H n e o a n o r o c j i o s a a a H -

H bi 4rz.-<-^+V.

nPEfl/IO>KEHHE 6 . r i p o 6 n e M a T o x n e c T B a(3)a n a K c a o n H T c a K n p o S n e M e p a s p e -

I I I H M O C T H a n a S c c n r H a n H 3 n p y K > m e f t Iwl ,

c a a n p o c a M H o H H c n a x , H e S o j i f a u i n x

,.«[""-;'-*]2. Cnanana PBCCMOTPHM BCHOMoraTenfaHyro rpynny j , KOTOpaa as-

naeTCfl CBo6oaHHM npOH3BeaenneM rpynnbi L <- n cso6oHHofi

rpynnw { /t} • /lK>6ofi anetvieHT H3 ^/ MO>Ker SbiTfa npeacTasneH B necoK-

paTHMoft sanncH Wy A0' H™ W, A*' Wa A^... WK A^^, rae W,, IV2,..., WK"

cnoBa KB ^ , w2 ,Vv^,. . , , w^^ /, <X /,...,cr,<_ /^= O , npaneM STO npeacTas -

neHHe eaHHCTBeHHO c TOHHOCTWO ao saMeHw noac/ios W. na cnosa, paB-

Hbie HM B i, . nemo aaaeTfa, HTO no niofioMy cnosy W us ^ yKaaaH-

HOS npeacTaaneHHe MOMOT 6biTfa nonyieHO c CHrHanHSHpyroinefl, He2, npHH6M OHO He flnHHHee IBM \ . Orcioaa nonyiaeM, HTO B rpyn

O CJIOJKHOCTH npoSneMM TOKaecTBa ana rpynn 37

ne f/ nna nraSoro t CHntHaa npoSneMa sxo>KfleHHa B nonrpynny

A L, A. pemaexca Ses ynnnHenHa cnoBa c CHrnanHSHpyioiHeH, He 6onb-

uieft, <JBM I Wl .i~ fc / T z3aMeTHM, KpOMe sxoro, HTO noarpynna A L^ A/ H3OMOp4)Ha rpyn -

ne L, , nosTOMy MOJKGM noCTpOHTt caoSonHoe npOHSBeaenae rpynn 'j H

L. ( L , - rpynna, HsoMOpejJHaa rpynne Ag npH

c o6i>eHHHeHHoft nonrpynnoii cnenyiomHM oSpaaoM:

MBCTO OHesuflHoe yTBep>KA6Hne: ^Z 6<2£ <-

KO xorna, Korna B rpynne K BbinonaeHO paseHCTBo:

— t> —La i. ?, —- i T— iA a, -DCL A. = a. OCL •

FIosTOMy H3 npe«no>KeHHa 1 nonynaeM, HTO c&B Torna H TonbKO

xorna BbinonHaerca nocneflsee paBencTBo B K^ • 3T(

cnpasennHBOCTfa npeflno>KeHHa 5 ana HBTHWX V(2t)

3AME4AHHE. Bee cooTHouieHna rpynnw K coxpaaaiOT cyMMy* £ i-t / i/BBCOB oyKB 6 H t? . Uo3TOMy, ecnH cnoBO W na rpynnw /C npHHaa-

nonrpynne c , TO W = ^ , rn.e QC =

3. AoKa>KeM cnpaBejuiHBocTt npennojKeHaa 6 n/ia rpynnbi

(1) flna CJIOB B oSpaayiomnx oanoft H3 rpynn *£/ HHH ^ npo6new:a

TO»necTBa peraaerca o6biHHOit MauiKHoft TfaropHHra c cnrHanH3Hpyiomeii, He

6onfauieft, HBM IWl . nosTOMy nycTt, y/ COCTOHT HS HecKonfaKHX

neft. Mo>KeM ciHTarb, HTO uHKJiHHecKoft nepecxaHOBKOil CJIOBO npHBeaeHO K

BHny ut V, Uz i^ . . . U.£ (Si , rae u^ - cnoao na ^ , c^- - CJIOBO aa L g ,

npHH6M Kawabift MHownTejifa OTJIKHBH or eaHHHuw.

(2) FIoKaKeM, HTO npoSneMa rojKaecTBa ana cnosa W pemaeTca aa

MauiHHe c S -ôpaKynoM c curHanHanpyiomeft IWl H aanpocaMU o nacnax,

--4

CHanana aaMexHM, HTO, ecnn VV^1-/, TO no KpaftHeft Mepe iiBa paa -

MHO>KHTena 5r,S2 npHHaflnewar oeteaHHeHHoil noarpynne. fleftcx -

, nanHHHe oflaoro Taxoro MHOJKHTena cneayex Ha jieMMbi 1.4. flna

onpeneneHHOCTH, nycrb STO MHo>KHTenfa 66^ . Ho rorna cnoBO

*L*l + <»^''-*AU'<*<'''U^*^

npHHao/re>KHT oSteaHHeHHoH noarpynne H, cornacno Tofi x.e neMMe 1.4, W

no Kpaftneft Mepe eme OHHH MHO»cHTenfa, npHHaflneacaimiH

38 M,K.BanH6B

nonrpynne. ECJIH KaKoft-naSo H3 3^, S_ -MHOJKHTejib H3 ^7 , TO

MOW6M CHHTaTb, HTO OH HM66T BH0 X #A . TflS Q - CJIOBO H3 ^ ̂ ._ tjr r£ -

riycTb iz - cnoBo onnoro HS BHHOB /L O'/L HJIH <2 , rae Q" - CHOBO HS

i, q . HaaoaeM CJIOBO g, Li - KOMnoHeHTOJS cnoaa a. . flcao, HTO t£ npn -

HaanejKHT o6teaHHeHHoft nonrpynne Toraa H TonbKO Toraa, Koraa a£- PC •

XOTH 6bi ana oanoro aa MHOxHTejiefl S,,3> ero L c - KOMnoHeHTa HMB -, , ^

, He 6onbinyK> IBM J — ! — ! — Li. . flna> L 2 J

er zuiHHy , He 6onbinyK> IBM — — — . . flna onpeneneHHOCTH nycTfa 3TO> L 2 J

Bepno nna .3 . IlHKJiHiecKoft nepecraHOBKoJi MOJKBM no6HTbca TOTO, HTO

or MHOKHTeneK U1 , (J"j. . Pa3bicKHBanne MHOxHTena £> . MO-

6biTt npoaeneHO cornacno aaMenaHHio 1 B n. 7 § 3 na Mauinne c *S -I iaopaKynoM c CHrHanHaapyionieft I\VI H aanpocaMH o nucnax He 6onfaiiiHx HBM

"f|w|L -MX] J

2 J 7

24 Iw l - lwlA- 2

^ JHycTfa a. - L — KOMnoneHTa cnoBa .3 . 3aMeHHB B W MHO*HTenfa

^ — i u>, *~z o ^ i3. Ha (2 , ecnn^. - MHO>KHTejib MS "y , HJIH Ha /t C'A, , ecna .5. -/ * ^

MHO5KHTeiIfa H3 "Ci nOnyHHM CnOBO W C MGHbUIHM HHCnOM

I"~|W L==p IW |~ lwL . floKaaaTenbcTBO yTBep>KneHHa (2) aa-

BepuiaeTca oneEHnHoft HHnyKHHeft no ~t

(3) ECJIH £=/ , TO npeanoxeHHe 6 oneBHaHbiM oopasoM BbiTexaeT H3

(2) , xaK KBK B 3TOM cjiynae o6a MHoacHTena c/^. H Vf npHHaane«aT o6te -

noarpynne, H, cnenoBarenbHO, W coaep>KHT no KpaftHefl Mepe2t

4) FlycTfa t > -f . flnfl sToro cnynaa noKameM, HTO, ecjm W — V, TO

> 2 1 , T.e. npeanoweHHe 6 cnpaseanHBO B Sonee cnnfaHoiS 4"opMe,

KOTopaa 6yfleT HcnonbaosaHa naMH B na/ifaHeftuieM B n. 6.

SaMeTHM, HTO flocTaTOHHO aoKaaaTb yTBep^neHHe nna CJIOB, y KOTO -

PMX nio6ofi H3 MHO>KHTeneft U • He npHHannexHT o6T»eziHHeHHOii noarpynne.C

fleftcTBHTenbHO, ecnn W coaepwHT no KpaflneH Mepe asa MHo>KHTena t/,-, t/-,

npHHaane>Kamne o6i>eaiiHeHHoft noarpynne, TO yTBepxneHHe OHeBHano, ran

KaK KaMawft HS STHX MHOKHTenefi coaepxHT no KpaiiHeii Mepe 2 1 Bxo>Kn.e -

HHfi SyKBbi A . Korna u—2 , o6a MHo»;HTenfl U.f , Uz oanoBpeMeHHo nH6o

npHHaanescaT o6i,eaHHeHHoft nonrpynne, jm6o eft He npHHaaneiKaT. HaKOHeu,

Koraa t->2 , n W conepKHT TOJIBKO OZIHH MHo>KHTenfa tt £ , npHHaane>tcamHH

o6i>enHHeHHoft noarpynne, saMenHB B W MHOKHTenfa U. ̂ Ha CHOBO HS L _ ,

paBHoe eMy, nonyHHM cnoso, HHCHO MHOJKHTeneil B KotopoM He MeHbiue ne-

Tbipex H KOTopoe He coaep*HT MHowHreneft HS j , npHHaane>Kainnx o6i,e-

O CJIOHCHOCTH npo6neMW TomaecTBa ana rpynn 38

noarpynne.

HraK, nycTb W He coaepaciiT MHOxcHTeneft U^ , npHHaanexcaiuHx o6te-

noArpynne.

a) PaccMOTpHM cnyiaft, noraa see MHOMCHxejiH tfy npaHaanexcaT o6t>e-

noarpynne. Toraa W Mo>KeM nepenncaTfa B BHae enosa VV HS

rpynnbi ^/ , HMeroiaero BHO

CJIOBO W no apyroMy MOJKHO npeAcraBHTfa B

rne n , ..., /?_- nenycTbie cnosa B cBo6oaHofl rpynne 7(. , > i ,..., £>p - cnosa

MS Li r i npaiSM Jn,.:. ,-Jp HenycTfci. Bonee xoro, McmeM npeononararfa, HTO

*> ~ , . . . , ~ > n'=^ H see /? . , KOTOpbie nonHocTbio npHHaanescar nexoTopOMy

1U • , Tox.e OTJTHHHbi oT eaHHHUbi (B npOTHBHOM cnyHae xaKHe noncnosa

MOJKHO 6biJio 6bi HsiHTfa H3 cnoBa W c caMoro Banana) . FIosTOMy nojiy -

HHM, HTO, T3K K3K W == ^ , TO XOTH 6bl OttHO H3 noaCJIOB F> . , KOTOpOS HeC tf

coaep^HTCfl B cnoBax U^ , paano eamnme. Toraa n ̂ HMeex ana Jm6o__^ — 1£ rr -- _ _. _

O. A. , n«6o A, n . , rae n . - CJIOBO BJA,) , coaep»cameeca B cocea -ci c. c ( c, L J ^ _z

H6M MHOKHTene U. £ ( /7 • H6 MOXeT HM6Tfa BHa /I. <-t g A- i T8K K8K B

3TOM cnyiae U. g 6bino 6bi paBHo eaHHHue). flna onpefleneHHOCTH,i — — — z.

BHa -^ tJ • . Toraa n , = A- , x.e. t-i p coaepscHT no Kpaftneft Mepe

BXO>KaeHHft

•* =#=uHRnHiecicyio nepecraHOBKy cnoaa W , nonyiHM CJIOBO W ,

HMeromee

BbimenpHBeaeHHbiM paccyxtaeHKHMH nonyHHM, HTO B W- — 1 •£ —

neKOTopoe noacnoBo ^ • Buna n , /t mn6o A. ^ . , Koxopoe pa-

BHO eaHHHue, H W coaepKHT no Kpaftnefl Mepe erne Z- Bxo>KfleHnft 6yKBbi

A . Ilpeanono>KHM, MTO W He coaepxcHT apyrnx 6yKB /I , KpoMe STHX

2 1- Bxo»caeHHii. FIoKaweM, HTO B STOM cnyiae W l^f. PaccMOTpHM naa

cnynaa: 1 ) n . npHHaanewHT MHo«HTenK> U. . n 2) n . npnaaane>KHT MHO-

>KHT6J1IO Ue,

~t 1/lento BHaeTb, HTO B cnynae 1) U^ HMeer ana A, Q A- H

^b * —ManbHbift oxpeaoK cnosa W , KOTOpbift Moatex coKpaTHTbca, STO Kg /L Qf&- ,

jU- *T.e. W^/. B cnynae 2) MaKCHManbHwfi OTpeaoK cnosa W , KOTOpwU MO-

40 M.K.BajiHeB

. —HC6T COKpaTHTbCH, 9TO JIW.6O U$ A Q , 6CJIH T7 . HM66T BHfl n. A. .

<3 A- t/s , 6CJIH Tlf HM66T BHH A.^ % / • T'e' Vv^/ •

6) FlycTb oSienHHeHHoft noarpynne npHHannexar MHOJKHTenH tA ,£>"..., £t.-T £ ^ ^ *

FIoncTaBnap B W BMBCTO acex MHOJKHTeneft &• cnoBa A. <7 • A, , nony -7 _ 7

HHM CnOBO W I B KOTOpOM H6T MHO>KHTeJieft H3 // , npHHaflJ16>KafflHX O6l>-

nonrpynne, npaneM HHCHO MHoacHTenefi B W He Menfauie nsyx.

B STOM cnyiae y cnosa W aon>KeH SBITB XOTH 6bi OAHH MHOMCHTenb ̂ us

"̂ , KOTOpwft npHHanêjKHT oSibemmeHHOft nonrpynne, r.e. pasen cnosy_7 <j

saaa A. a A, , rue ae A7^ . HCHO, HTO STOT MHo»HTejib HMGBT BHH

-/ -t zTorna paseHCTso: 5 A Â- =^ CBOAHT cnynafi 6) K cnynaio a).

,x ,4. Hcxofla H3 rpynnti f\ nocrpOHM rpynny K . HycTfa

K , o6o3HanaeT rpynny \K ,/-<-', & =// \ Torna K ' Z+

- r SnonyiaercH HS K ynaneHHeM oSpasywmefl & , npanSM BO see on -5 .̂ (Zz +• f) T i

penenfljomne cooxHouieHHa rpynnw K BMSCTO & noacTaBjiaeTcs/^ .

HMeer Mecro cneoyiomaH

J1EMMA 4.1. F I p o S n e M a r o w a e c T B a n n aX (2z+ D

r p y n n b i / \a c c u r H a n H S H -

p y K ) in e f t |wl K n p o 6 n e M e r o > K n e c T B a n n a

K(™ .

AOKA3ATE/lbCTBO. Ronrpynna J ^ l rpynnu K( HsnaeTCH CBO-«oonHOH, nosTOMy K MO>KHO paccMarpHBaTt KBK CBOOonnoe nponsBe-

-c oStenHneHHoft nonrpynnofi rpynn K H \ Oycxfa w - cno-

.. <2z + /; S l^JBO B oopasyroraHx rpynnw K .

a) ECJIH W - cnoBO B oSpasyjomnx onnoft HS rpynn K

\U\ TO yTsepwneHHe neMMH

6) riycTfa W COCTOHT us HecKonbKHX MHOjKHTenefi H uHKnunecKoft ne-

npHBeaeno K Bany W / X / W W - X ^ * .rnew-^/ (C=-f2...,K.),I J c. K f - 7 1 ' '

(L—1,2 ..... X ) , W /,...,W /C. - cnoaa HS rpynnw ̂

B) MOJKSM CHHTaTb, HTO &.= ± f (L=^Z,...,K) , T3K K3K B

THBHOM cnynae noncnosa BHfla LL~ MOJKHO saMeHHTb 6yKBaMH ^ . ECJIH

K. = / , TO V/^= / . FIosTOMy 6yneM CHHraTb, HTO K > / . PaccyxneHHe,

aHanorHHHOe TOMy, KOTOpoe nposeneHO B HBCTH (2) nyHKTa 3 noKaaw-

BaeT, HTO B 3TOM cnyHae, ecna W= / i TO Haftaerca MHOKHTenb w-Li

O CJIOMCHOCTH npo6jieMbi TowflecTsa ana rpynn 41

1) |y/. | 4. - 2) y/- £ | -6 \ixo 1) |y/. | 4. - 2) y/- £ | - • PaabicKHsaHHe xaxoro MHO-

jKHxena, cornacno saMeiaHHio us nyHKxa 2 csoaHXca K pememiio npo6neMbi

is (ZZ) xTO>KaecTBa ana cnoaa HS K , HMeroinero anHHy He oonfauiyro, HSM

|y/|— 2- Oycxfa W- = 6 (cornacHO TOMy >Ke saMenaHHio us nymcxa 2,Lf

|ccl •C |WJ ) . ByaeM cinxarb, HXO t. > / (axoro aceraa MO»HO no6nTfaca UHK-

nHiecKOft nepecTaHOBKafl cnosa yf ) . SaMenaa B \ noncnoso \V^ cno-2<X , « • ,-t- 2 of + ayBOM /x , H saMenaa BHOBt nonyneHHoe ncmcnoBO LL *• ' aa

~ jy.*- °</-/+°f/. .* 7cnoBO £j 2 > nonyiHM CHOBO W c MenfainHM HHCJIOM MHO>KHTe-

neft, npHH6M lw*l<- lWl — 2 • floKaaaxejibCTBO neMMbi aaBepuiaexca oie-

BHHHOfi HHflyKUHeft HO K(2i + i)

5. CnpaBefljiHBOCTb npeano»eHHa 5 nna rpynnbi K ycMarpn -

Baerca HS OHSBHUHoro aaMenaHna: pasencTBO A. CL &Ci /t =-Q.~l"DCii'.,BbinonHHeTca B rpynne K roraa H rojibKo H xontKo xoraa, noraa

?Clai&ai?J-=a.-L[JLtciL B rpynne K<* ̂ " .r (2z+/>

6. floicaKeM ana rpynnw K npeanoweHHe 6. PaccMOxpHM 2

B03MO)KHbIX

1) W He coaepMHX BxojKaeHHH 6yKBbi U. , x.e. W - cnoao us rpyn-

nw K

a) Ecna W - cnoso B o6pa3yiofflHX OBHOH HS rpynn ^ KJIK L, ,

TO npo6neMa xoKaecxsa ana w pemaexca Ha o6biHHofi MauiHHe c CHrna-

nH3Hpyiomefl Iw I 2.

6) Ilycxb W HMeex BHA U.^- , rae U-^^, (J-z£ L ~ • Tor-

aa. Qcn.w.u.,3. P , xo W^= / . TaK KaK tl, He coaep^HX 6yKBbi -f> ,xoz ' s / *•cornacHO saMenaHHro 2 HS n. 7 § 3 sonpoc o npHHaaneacHOcxH U.z K P

2_ npemaexca Ha o6biHHHH Mamnne c curnajiHSHpyioiiieH IWI . EcnHi/, eAv ,

_ £ rr

B W noacjioso u.. na cnoao A. <J., A i CBOflHM Bonpoc K cny -

a).

B) v/ HMeex BHB

cnoBa H3 ) &,&.,...,•(?, - cnoBa H3 / s

OT enHHHUbi. 3xox cnynaft paccMOxpen B nymcxe 3 npn noxaaa -

npeaJioweHHfl 6 ana rpynnw K. Ha mare (4). /lerico 3a-

HXO nonyieHHbie xaM OUOHKH aocxaxoHHbi ana sxoro cny -

naa.

2) Flycxb W conepscHX Bxo>KneHHa 6yxBbi u. . PaccMOxpMM VV

saK CJIOBO rpynnw K c . ECJIH vs/ conepacHx xoxa 6w oano noa -±2 i T ,CJIOBO BHaa LL , xo, SaMenaa LL Ha t> , yMCHbrnaeM anHHy cjiosaNA'

Ha eauHnuy, H xpe6yeMbie OUOHKH Bbixexaiox H3 neMMbi 4.1. B HPOXHBHOM

42 M.K.BanneB

cnynae HMeeM cnyiaJl B) us aoKaaarenfaCTBa neMMbi 4.1 H KaK raM no -

KaaaHO, peiuemie npoSneMbi TOJKflecTBa ana W CBOflHtca K peuieHHio npo-(2z)

6neMbi xo>KflecTBa nna CHOB rpynnw /C , HMeromHx anHHy He 6onfaiuyio

H6M (Wl — 2. OpeflJioxemie 6 noKaaano nojiHOCTbio.

7. flaflHM OKOHHarenfaHoe nocxpoeHne rpynnbi K _ . ConocraEHM MHO-

5 nerbipe p.n. MHowecrsa: S_= I x| (-^X-l- 4) £ S|

S, -

Bbi6epeM B KanecTse /C. cBo6onnoe npoH3BeaeHHe rpynn /C , /^ ,.,(4; -,(3") S ^3J ..MS°<5) '

/< , /< j. (HMeexcH B BHAy, HTO oyKBbi rpynn ft , K. , K nepeH -^2. ^3 5/ SZ S3

xaKHM o6pa3OM, HTO HHKaKaa napa coMHOxHTeneft cso6oflHoro

He HMeer o6mnx 6yKB) .

1) reopeMbi 1 OHeannHbiM o6paaoM BbixeKaex us npen -

no»eHna 5, yTBep»neHHe 2) - us npennoweHHa 6.

B aamiroieHHe Bbipaxaio 6naronapHOCTfa B.A.TpaxreH6pOTy H H.A.Bo-

Kyrio aa BHHMaTenbHoe npOHTeane pyKonnca H pan nonesnux

HanpaBneHHbix K ynyHiueHHio

FIocTynmia B

12. yn. 1968 r.

/ i H r e p a r y p a

1. O.C.HOBHKOB, O6 anropHTMHHecKofl HepaspeuiKMOcra npo6neMbicnos B rpynnax, Tpyflw Mar. HncTHTyra HM. CxeKJiOBa, 44

(1955).

2. W.W.BOQNE, The word problem, Ann. Math., 70 (1959) K 2,207-265.

3. G.HIGMAW, Subgroup* of finitely presented groups, Proc.Royal. Soo., A 262 O961), 455-*75.

4. J.L.BBITTOH, The word problem, Ann. Math, 77, K 1 O963),16-32.

5. A.A.4>PHflMAH, CreneHH HepaspeuiHMocTH npo6neMbiana KOHeino onpeneneHHbix rpynn, M., "Hayxa" C1967).

6. C.B.T. CLAPHAM, Finitely presented groups with word prob-lems of arbitrary degrees of unaolvability. , Proc. Load. Math. Soe. ,XIV, 56 (1964), 633-676.

7. W.w. BOONS, Word problem and recursively enumerable degreesof unaolvability, A sequel on finitely presented groups, Ann. Math.,84, 1C 1 (1966), 49-84.

O CJIOJKHOCTH npo8n«Mbi TOxcnecTBa ana rpynn 43

8. Jl.A.BOKyTb, O6 oaHOM caoftcTse rpynn Byua, AnreSpa H norn-Ka, 5, No 5 (1966), 5-23.

9. B.A.TPAXTEHBPOT, CJIOXHOCT!. anropHTMOB H BbiHHcnemifi, Ho-Bocn6npcK, 1967.

10 A.GRZEGORCZYK, SoBe classes of recursive functions, Rozpra-wy Math. (1953), vol. *.

11. F.B.CANNONITO, Hierarchies of computable groups and theword problem, J. Symb. Logic, 31 (1966), 3, 376-392.

12. B.A.TPAXTEHBPOT, O CJIO>KHOCTH anropHTMOB caeaeHHa B KOHCT-pyKHHH HoBHKOBa-ByHa. - flaHHbift c6opHHK, crp. 93-128.

13. M.K.BA/1HEB, O6 oanoft reopeMe r.XHrMana, Anre6pa H nornKa,7, No 3 (1967), CTP. 9-22.

14. M.DAVIS, Cooputability and unsolvability, Me. Graw. Hill,Hew 5fork, 1958.

15. A.r.KyPOUl, TeopHH rpynn, M., 'Hayna', H3fl. 3 (1967).

Documents

Anre6pa H normca, 8, Ns 1 (1969), 5. YAK 51.01:518.5:519.45 …math.nsc.ru/~alglog/01-10/08/08N1-1.pdf · 2010-08-12 · Anre6pa H normca, 8, Ns 1 (1969), 5. YAK 51.01:518.5:519.45