Question
Let $H$ be a Sylow $p$ -subgroup of $G$. Prove that $H$ is the only Sylow $p$ -subgroup of $G$ contained in $N(H)$.
Step 1
We know that $H$ is a Sylow $p$-subgroup of $G$, so $H$ is a $p$-group and $|H| = p^n$ for some $n \ge 1$. Show more…
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Let $G$ be an abelian group. If $H=\left\{x \in G: x=x^{-1}\right\}$, that is, $H$ consists of all the elements of $G$ which are their own inverses, prove that $H$ is a subgroup of $G$.
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