is a cyclic subgroup of ; let's say it has order . By Lagrange, , which means for some integer .
So then .
12) Let G be a group of finite order n. Prove that a^n = e for all a in G.
This is what I have so far. I believe I should use Lagrange's Theorem but I get stuck.
Proof. Let G be a group of finite order n and a be in G. Since a is in G, then a^-1 is also in G. ...