Let A be an abelian group. Show K = {a in A | a^{n} = 1} is a subgroup of A
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To show that K is a subgroup of A, we need to show three things: Show more…
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Let $G$ be an abelian group. Let $H$ be a subgroup of $G$, and let $K$ consist of all the elements $x$ in $G$ such that some power of $x$ is in $H$. That is, $K=\left\{x \in G:\right.$ for some integer $\left.n>0, x^{n} \in H\right\}$. Prove that $K$ is a subgroup of $G$.
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