Open AccessProfinite groups with an automorphism whose fixed points are right Engel
Author(s) -
Cristina Acciarri,
E. I. Khukhro,
Pavel Shumyatsky
Publication year - 2019
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14519
Subject(s) - automorphism , mathematics , fixed point , profinite group , pure mathematics , group (periodic table) , mathematical analysis , physics , quantum mechanics
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.
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