Almost regular automorphisms of finite groups of bounded rank
type: Item
instance of: scholarly article
title: Almost regular automorphisms of finite groups of bounded rank
zbMATH Open document ID: 0882.20014
DOI: 10.1007/BF02106748
published in: Siberian Mathematical Journal
publication date: 1998-03-09T00:00:00Z
review text: It is proved that if a finite or solvable group of rank \(r\) admits an automorphism of order coprime to the order of the group with exactly \(m\) fixed points, then the group has a solvable subgroup of \((r,m)\)-bounded index whose derived length is bounded in terms of \(r\) only. Earlier \textit{A. Shalev} proved under the same assumptions that the group has a solvable subgroup of \((r,m)\)-bounded index whose derived length is \((r,m)\)-bounded [Isr. J. Math. 82, No. 1-3 395-404 (1993; Zbl 0817.20026)]. The proof is reduced to the case of finite \(p\)-groups. It is based on using Shalev's above-mentioned result and the theory of powerful \(p\)-groups.
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20F16
zbMATH DE Number: 1023897
zbMATH Keywords: almost regular automorphisms
zbMATH Keywords: solvable subgroups of bounded index
zbMATH Keywords: powerful \(p\)-groups
zbMATH Keywords: derived lengths
author: Evgenii I. Khukhro
reviewed by: N. Yu. Makarenko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1023897