# Math Help - Prove that a^(n) = e for all a in G.

1. ## Prove that a^(n) = e for all a in G.

Let G be a group of finite order n. Prove that a^(n) = e for all a in G.

2. Originally Posted by rainyice
Let G be a group of finite order n. Prove that a^(n) = e for all a in G.

By Lagrange's theorem, and $a^k=e\Longrightarrow a^n=(a^k)^x=\ldots$

Tonio