Some periodic groups admitting a finite regular automorphism of even order
type: Item
instance of: scholarly article
title: Some periodic groups admitting a finite regular automorphism of even order
zbMATH Open document ID: 1443.20066
author: Yanyan Li
published in: Algebra and Logic
publication date: 2019-12-06T00:00:00Z
full work available at URL: http://elib.sfu-kras.ru/handle/2311/128604
review text: The authors are interested in studying infinite groups \(G\) with regular automorphisms \(\phi\) of finite order \(2p\) where \(p\) is an odd prime, the finite case having been studied extensively some 50 years ago, mainly by B. Fischer. The main interest here is in the case where \(G\) is locally finite, but the authors can regularly relax this assumption to periodic groups satisfying hypotheses such as every element of \(G\) lies in a finite \(\phi\)-invariant subgroup and the centralizers of involutions are locally finite. The vast bulk of this paper concerns groups \(H\) with elements \(i\) and \(a\), where \(i\) has order 2 and \(a\) has order \(p>2\), such that for every \(g\in H\backslash C_H(i)\) the subgroup \(\langle i,a^g\rangle\) is a finite Frobenius group with the non-normal factor of even order and containing \(a g\). The connection with \(G\) and \(\phi\) above is that \(H\) might be the split extension of \(G\) by \(\langle\phi\rangle\).
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E36
zbMATH DE Number: 7140937
zbMATH Keywords: periodic group
zbMATH Keywords: locally finite group
zbMATH Keywords: regular automorphism
reviewed by: B. A. F. Wehrfritz
MaRDI profile type: Publication
OpenAlex ID: W2947361323
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Wikidata QID: Q127706660
DOI: 10.1007/S10469-019-09521-7
description: scientific article; zbMATH DE number 7140937