Find the minimum of all positive integers m such that every sigma in S_9 (Sigma in A_9) satisfies sigma^ n = 1.

Find 4 different subgroups of S_4, isomorphic to S_3, and nine isomorphic to S_2. ( I dont need all the subgroups just how to find them isomorphic)

Let G be a subgroup of S_5. Prove that if G contains a 5-Cycle and a 2-Cycle, then G = S_5.