Let t be an element of S be the cycle (1,2....k) of length k with k<=n.

a) prove that if a is an element of S then ata^-1=(a(1),a(2),...,a(k)). Thus ata^-1 is a cycle of length k.

b)let b be any cycle of length k. Prove there exists a permutation a an element of S such that ata^-1=b.

We assume t is an element of S and a is an element S.

By definition of elements of S if t is in S, we have a determined by t(1), t(2),...,t(n)

Furthermore if a is in S, we have a(1), a(2)....a(n).

That's as far as I get.