## Elements of Finite Order of an Abelian Group form a Subgroup

## Problem 522

Let $G$ be an abelian group and let $H$ be the subset of $G$ consisting of all elements of $G$ of finite order. That is,

\[H=\{ a\in G \mid \text{the order of $a$ is finite}\}.\]

Prove that $H$ is a subgroup of $G$.

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