Almost fixed-point-free automorphisms of prime order.
type: Item
instance of: scholarly article
title: Almost fixed-point-free automorphisms of prime order.
zbMATH Open document ID: 1245.20037
published in: Central European Journal of Mathematics
publication date: 2012-01-16T00:00:00Z
review text: The author discusses groups \(G\) possessing an automorphism \(\phi\) of prime order \(p\) in which \(C_G(\phi)\) is finite of order \(n\). In this context the author discusses groups of finite Hirsch number. A group \(G\) has finite Hirsch number if it has a series of finite length such that each factor of the series is either locally finite or infinite cyclic, the Hirsch number being the number of infinite cyclic factors in this series. As an example of some of the results, the author proves that such a group \(G\) with such an automorphism has a soluble characteristic subgroup of finite index of \((p,n)\)-bounded derived length. He also proves that if \(G\) is soluble of finite rank with such an automorphism then \(G\) has a characteristic subgroup of finite index that is nilpotent of class at most a function of \(p\).
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 5997907
zbMATH Keywords: soluble groups
zbMATH Keywords: groups of finite Hirsch number
zbMATH Keywords: groups of finite rank
zbMATH Keywords: automorphisms of prime order
zbMATH Keywords: fixed-point-free automorphisms
zbMATH Keywords: characteristic subgroups of finite index
author: B. A. F. Wehrfritz
reviewed by: Martyn Dixon
MaRDI profile type: Publication
full work available at URL: s11533-011-0017-z
OpenAlex ID: W2004251139
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DOI: 10.2478/S11533-011-0017-Z
description: scientific article; zbMATH DE number 5997907