PROFINITE GROUPS WITH AN AUTOMORPHISM WHOSE FIXED POINTS ARE RIGHT ENGEL

被引：4

作者：

Acciarri, C. ^{[1
]}

Khukhro, E., I ^{[2
,3
]}

Shumyatsky, P. ^{[1
]}

机构：

[1] Univ Brasilia, Dept Math, BR-70910900 Brasilia, DF, Brazil

[2] Univ Lincoln, Charlotte Scott Res Ctr Algebra, Lincoln LN6 7TS, England

[3] Sobolev Inst Math, Novosibirsk 630090, Russia

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 147卷 / 09期

基金：

俄罗斯科学基金会;

关键词：

Profinite groups; finite groups; Engel condition; locally nilpotent groups; LIE-ALGEBRAS; IDENTITIES;

D O I：

10.1090/proc/14519

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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

引用

页码：3691 / 3703

页数：13

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