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

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 ...

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.

plaese give me the proof