Profinite groups and the fixed points of coprime automorphisms

Cristina Acciarri; Pavel Shumyatsky

doi:10.1016/j.jalgebra.2016.01.010

paper

Profinite groups and the fixed points of coprime automorphisms

arXiv:1703.00988 · doi:10.1016/j.jalgebra.2016.01.010

Abstract

The main result of the paper is the following theorem. Let $q$ be a prime and $A$ an elementary abelian group of order $q^{3}$ . Suppose that $A$ acts coprimely on a profinite group $G$ and assume that $C_{G} (a)$ is locally nilpotent for each $a \in A^{#}$ . Then the group $G$ is locally nilpotent.

arXiv admin note: substantial text overlap with arXiv:1702.02899