Somnath posted an Question
April 07, 2021 • 18:15 pm 30 points
  • IIT JAM
  • Mathematics (MA)

)) prove that every proper subgroup of a symmetric group s, is cyclic.

)) Prove that every proper subgroup of a symmetric group S, is cyclic.

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    Swapnajit das best-answer

    order of S3 is 6. Any proper subgroup of S3 must have order 1,2,3 .because by lagranges theorem, we know order of subgroup divides of order of group. Now being all are prime, all subgroups are cyclic because any group of order prime is cyclic

  • Kiran goswami

    any proper subgroup of S3 must have 1, 2 or 3 elements. (Order of subgroup must divide order of the group.) And any group of prime order is cyclic.

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