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

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

    By Lagrange's theorem, |<a>|\mid |G|\Longrightarrow ord(a)=k\mid n\Longrightarrow n=xk\,,\,\,x\in\mathbb{N} and a^k=e\Longrightarrow a^n=(a^k)^x=\ldots

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