On locally graded barely transitive groups.
type: Item
instance of: scholarly article
title: On locally graded barely transitive groups.
zbMATH Open document ID: 1279.20001
author: Cansu Betin
author: Mahmut Kuzucuoğlu
published in: Central European Journal of Mathematics
publication date: 2013-06-14T00:00:00Z
review text: Let \(G\) be a transitive permutation group on an infinite set. Then \(G\) is said to be barely transitive if every orbit of every proper subgroup of \(G\) is finite. The second author has considered such \(G\) several times over last 20 years or more. Here the authors' main theorem is the following. If \(G\) is barely transitive, then \(G\) is totally imprimitive if and only if \(G\) is locally graded. (\(G\) is totally imprimitive if there is an ascending chain of proper blocks of \(G\) with no maximal member; \(G\) is locally graded if every nontrivial finitely generated subgroup of \(G\) has a proper subgroup of finite index.) In particular every locally finite, barely transitive group is totally imprimitive. The authors continue by producing fairly detailed descriptions of certain types of barely transitive groups.
Mathematics Subject Classification ID: 20B07
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E25
zbMATH DE Number: 6176166
zbMATH Keywords: infinite permutation groups
zbMATH Keywords: barely transitive groups
zbMATH Keywords: locally graded groups
zbMATH Keywords: locally finite groups
reviewed by: B. A. F. Wehrfritz
MaRDI profile type: Publication
full work available at URL: s11533-013-0240-x
OpenAlex ID: W1993632179
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DOI: 10.2478/S11533-013-0240-X
description: scientific article; zbMATH DE number 6176166