Antima Jangid posted an Question
January 09, 2022 • 06:31 am 30 points
  • IIT JAM
  • Mathematics (MA)

116. how many 3-sylow subgroups does the symmetric group s have? (a)8 (c) 2 (b) 4 (d) 1 1 (net dec. 2019 2nd pp) 4

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  • Anonymous User Best Answer

    B Any Sylow 3-subgroup of S4 has size 3 and is therefore generated by an element of order 3. Hence, the Sylow 3-subgroups are specified by elements of order 3 that generate the same subgroup. Thus, the Sylow 3-subgroups of S4are generated by H1 = (123) H2 =(124) H3 = (134) H4 = (234)

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