This exercise determines when two elements of sn are conjugate.
(a) show that for any k cycle (a1, ..ak) e sn, and for any permutation π n, we have hint: as always, first look at some examples for small n and k. both sides are permutations (i. e., bijective maps defined on 11, , show that they are the same maps by showing that they do the same thing.
(b) show that for any two k cycles, (ai. ak) and (bi, b2. . , bk) in sn there is a permutation π e s, such that