Умножение симметрий и преобразований

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    MULTIPLICATIONOF SYMMETRIESAND TRANSFORMATIONS

    A. Yu. OLSHANSKII

    This paper introducesthe group theoreticalpoint of view of symme-tries and transformations.Symmetries of polynomi-als are used as a defini-tion for permutationssign, which is appliedafterwards to a puzzle.Multiplication of symme-tries is quite different fromusual numerical opera-tions. Therefore a cal-culus arises which leadsto general notions of thegroup theory.

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  • , 5, 1996118

    h = f1 f2 h(1) = f1( f2(1)). 2 , f2(1) = 3, f1(3) = 3, h(1) = 3. -: h(2) = 1 h(3) = 2. , f1 f2 , f5 2, , f1 f2 = f5. , f2 f1 = f4, f1 f2 , , , f4 f5: f4 f5 = f5 f4.

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  • , 5, 1996120

    - - h ( , n > 1). - hf1, , hfs ( hfi = hfj h- 1 - fi = fj). 1 s , , g1, , gt. , s # t. , hg1, , hgt, : t # s. , s = t, 3 , s + t = n!. ,

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