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Questions about the branch of algebra that deals with groups.

2 votes
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Split extension of finite group and Sylow subgroup by abelian $p$-group

Let $p$ be a prime and let $A$ be an abelian normal $p$-subgroup of a finite group $G$. Hence, for any Sylow $p$-subgroup $H$ of $G$, it holds that $A$ is contained in $H$ and so $A$ is a normal subgr …