Question
If $H$ is a normal subgroup of $G$ and $|H|=2$, prove that $H$ is contained in the center of $G$.
Step 1
Since $|H|=2$, there are only two elements in $H$: the identity element $e$ and another element $h$ such that $h^2 = e$. Show more…
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Let $G$ be an abelian group. Let $H$ be a subgroup of $G$, and let $K=\left\{x \in G: x^{2} \in H\right\}$. Prove that $K$ is a subgroup of $G$.
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