Profinite groups and the fixed points of coprime automorphisms

Cristina Acciarri; Pavel Shumyatsky

doi:10.1016/j.jalgebra.2016.01.010

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arXiv · 1703.00988

Profinite groups and the fixed points of coprime automorphisms

Cristina Acciarri·Pavel Shumyatsky

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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.

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BibTeX RIS

Cristina Acciarri, Pavel Shumyatsky. 2017-03-02. Profinite groups and the fixed points of coprime automorphisms. https://doi.org/10.1016/j.jalgebra.2016.01.010

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