Double coset decomposition of groups
type: Item
instance of: scholarly article
title: Double coset decomposition of groups
zbMATH Open document ID: 0944.20024
published in: Journal of Algebra
publication date: 2000-06-21T00:00:00Z
review text: The author shows that if \(G\) is a group which is either residually finite or word hyperbolic and if \(G\) can be decomposed as a finite union of double cosets of a cyclic subgroup, then \(G\) is virtually cyclic. The work answers for a large class of groups a question of M. Dunwoody. The author applies then this result to the study of Frobenius groups (that is, groups acting transitively on a set of cardinality \(\geq 2\) such that the only element which fixes two distinct points is the identity). He shows finally that if \(G\) is an arbitrary group and if \(H\) is a subgroup of \(G\) and if \(G\) is a finite union of double cosets of \(H\), then no subgroup of \(G\) can split over a subgroup commensurable with \(H\).
Mathematics Subject Classification ID: 20F67
Mathematics Subject Classification ID: 20E26
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E06
zbMATH DE Number: 1384472
zbMATH Keywords: word hyperbolic groups
zbMATH Keywords: residually finite groups
zbMATH Keywords: Frobenius groups
zbMATH Keywords: unions of double cosets
zbMATH Keywords: amalgamations
zbMATH Keywords: HNN extensions
author: Graham Niblo
reviewed by: Athanase Papadopoulos
MaRDI profile type: Publication
full work available at URL: jabr.1999.7935
OpenAlex ID: W1993706089
cites work: Q4865842
cites work: Q4867098
cites work: Q3772406
cites work: Q4400506
cites work: Q4282627
cites work: \(\pi_1\)-injective surfaces in graph manifolds
cites work: Ends of pairs of groups
DOI: 10.1006/JABR.1999.7935
description: scientific article; zbMATH DE number 1384472