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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Item Type: | Article |
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Item Status: | Live Archive |
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 |
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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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