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Profinite groups with an automorphism whose fixed points are right Engel

Acciarri, Christina, Khukhro, Evgeny and Shumyatsky, Pavel (2019) Profinite groups with an automorphism whose fixed points are right Engel. Proceedings of the American Mathematical Society, 147 (9). pp. 3691-3703. ISSN 0002-9939

Full content URL: https://doi.org/10.1090/proc/14519

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Profinite groups with an automorphism whose fixed points are right Engel
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Abstract

An element g of a group G is said to be right Engel if for every x ∈ G there is a number n = n(g, x) such that [g, nx] = 1. We prove that if a profinite group G admits a coprime automorphism ϕ of prime order such that every fixed point of ϕ is a
right Engel element, then G is locally nilpotent.

Keywords:Profinite groups, finite groups, Engel condition, locally nilpotent groups
Subjects:G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
ID Code:34600
Deposited On:01 Feb 2019 13:14

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