1. The problem statement, all variables and given/known data 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. 2. Relevant equations 3. The attempt at a solution 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.