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

Alireza Abdollahi; S. Mohsen Ghoraishi

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

Group Theory 2013-07-23 v1

Authors: Alireza Abdollahi , S. Mohsen Ghoraishi

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 $p^2$ .

Keywords

automorphism groups finite groups finite group theory

Cite

@article{arxiv.1307.5417,
  title  = {$p$-Groups for which each outer $p$-automorphism centralizes only $p$ elements},
  author = {Alireza Abdollahi and S. Mohsen Ghoraishi},
  journal= {arXiv preprint arXiv:1307.5417},
  year   = {2013}
}

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