How do I prove that finitely generated group with $g^2=1$ is finite? Let $G$ be a finitely generated group.
Assume for all $g\in G, g^2=e$.
Then, how do I show that $G$ is actually finite?
I don't know where to start..

Let $\Bbb K=\Bbb Z/\Bbb Z$. And define $\Bbb K\times G\to G$ by $(k,g)\mapsto g^k$.
Hence $G$ is a $\Bbb K$ vector space with finite dimension . so $G$ is finite.
