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

Authors
Type
Preprint
Publication Date
Jul 20, 2013
Submission Date
Jul 20, 2013
Identifiers
arXiv ID: 1307.5417
Source
arXiv
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 $p^2$.