Fixed-point-free 2-finite automorphism groups.
type: Item
instance of: scholarly article
title: Fixed-point-free 2-finite automorphism groups.
zbMATH Open document ID: 1241.20036
author: Theo Grundhöfer
author: Enrico Jabara
published in: Archiv der Mathematik
publication date: 2011-10-25T00:00:00Z
full work available at URL: http://hdl.handle.net/10278/24442
review text: A group \(G\) is called \(n\)-finite if any \(n\) elements of \(G\) generate a finite subgroup. The main result of the paper states that a fixed-point-free group \(G\) of automorphisms of an Abelian \(2\)-finite group is locally finite. Earlier \textit{A. I. Sozutov} [in Sib. Math. J. 35, No. 4, 795-801 (1994); translation from Sib. Mat. Zh. 35, No. 4, 893-901 (1994; Zbl 0851.20039)] characterized the subgroups of \(G\) generated by all elements of prime order. The main theorem implies that a nearfield with \(2\)-finite multiplicative group is a locally finite nearfield, and a sharply \(2\)-transitive \(2\)-finite permutation group is locally finite.
reviewed by: N. Yu. Makarenko
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20B22
Mathematics Subject Classification ID: 12K05
zbMATH DE Number: 5963406
zbMATH Keywords: fixed-point-free automorphisms
zbMATH Keywords: 2-finite groups
zbMATH Keywords: locally finite groups
zbMATH Keywords: automorphism groups
zbMATH Keywords: nearfields
zbMATH Keywords: sharply 2-transitive groups
MaRDI profile type: Publication
OpenAlex ID: W2088782821
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DOI: 10.1007/S00013-011-0284-8
description: scientific article; zbMATH DE number 5963406