Введение в теорию групп. Задачи и теоремы. Часть 1. Тронин С.Н. - 63 стр.

 3.71.   dANA GRUPPA G S \LEMENTAMI
  1 R R2  R3 S S 2 S 3 SR SR2  SR3  S 2R S 2R2  S 2R3 S 3R S 3R2  S 3R3 
KOTORYE UDOWLETWORQ@T SLEDU@]IM SOOTNOENIQM:
                      R4 = S 4 = 1 RS = S 3R3  R3S = S 3R:
  1) nAJTI W QWNOM WIDE KLASSY SOPRQVENNYH \LEMENTOW G .
  2) nAJTI CENTR G .
  3) nAJTI PORQDOK \LEMENTA X = SR2 .
  4) nAJTI LEWYE I PRAWYE SMEVNYE KLASSY G PO H = hX i .
  5) nAJTI KOMMUTANT G G] .
 3.72.   dANA GRUPPA G S \LEMENTAMI
           1 R S T RS RT TR SR ST TS A A2 A3 B C D
KOTORYE UDOWLETWORQ@T SLEDU@]IM SOOTNOENIQM:
         R2 = S 2 = T 2 = 1 RST = TRS = STR (RST )4 = 1
               TRT = SRS RTR = STS TST = RSR
              A = RST B = TRT C = RTR D = TST:
  1) nAJTI W QWNOM WIDE KLASSY SOPRQVENNYH \LEMENTOW G .
  2) nAJTI CENTR G .
  3) nAJTI PORQDOK \LEMENTA X = RS .
  4) nAJTI LEWYE I PRAWYE SMEVNYE KLASSY G PO H = hX i .
  5) nAJTI KOMMUTANT G G] .
uKAZANIE: DOKAZATX PREDWARITELXNO, ^TO AR = RA , AS = SA , AT =
TA .
 3.73.   dANA GRUPPA G S \LEMENTAMI
       1 S S 2 S 3 S 4 S 5 S 6 S 7 T ST S 2T S 3T S 4T S 5T S 6T S 7T
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