Let G be a group of finite order n. Prove that a^(n) = e for all a in G.
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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, $\displaystyle |<a>|\mid |G|\Longrightarrow ord(a)=k\mid n\Longrightarrow n=xk\,,\,\,x\in\mathbb{N}$ and $\displaystyle a^k=e\Longrightarrow a^n=(a^k)^x=\ldots$ Tonio
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