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$p$-Groups for which each outer $p$-automorphism centralizes only $p$ elements

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Type
Preprint
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arXiv ID: 1307.5417
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arXiv
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Abstract

An automorphism of a group is called outer if it is not an inner automorphism. Let $G$ be a finite $p$-group. Then for every outer $p$-automorphism $\phi$ of $G$ the subgroup $C_G(\phi)=\{x\in G \;|\; x^\phi=x\}$ has order $p$ if and only if $G$ is of order at most $p^2$.

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