Can someones tells me how to prove these theorems.
1. Prove that if G is a group of order p^2 (p is a prime) and G is not cyclic, then a^p = e (identity element) for each a E(belongs to) G.
2. Prove that if H is a subgroup of G, [G:H]=2, a, b E G, a not E H and b not E H, then ab E H.
3...