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Questions about the group of automorphisms of any mathematical object $X$ endowed with a given structure, i.e the group of all bijective maps from $X$ to itself preserving this structure, and hence helping study it further and understand it better.

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Structure of Sylow $p$-subgroup of $G$ with given property

I think the first part is correct as stated, by the Burnside argument. Let $V=\langle z\rangle,$ and let $W$ be a subgroup of order $p$ of $Z(P).$ Since in particular $W\subseteq P,$ there is $a\in A$ …
Tom WIlde's user avatar
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