The Tits alternative for short generalized tetrahedron groups.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1260.20053
publication date: 2012-09-04T00:00:00Z
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E06
zbMATH DE Number: 6076257
zbMATH Keywords: generalized tetrahedron groups
zbMATH Keywords: generalized triangle groups
zbMATH Keywords: Tits alternative
zbMATH Keywords: triangles of groups
zbMATH Keywords: Fortsetzungssatz
zbMATH Keywords: free subgroups
describes a project that uses: GAP
MaRDI profile type: Publication
author: B. Fine
author: A. Hulpke
author: V. große Rebel
author: Gerhard Rosenberger
author: S. Schauerte
title: The Tits alternative for short generalized tetrahedron groups.
published in: Scientia. Series A: Mathematical Sciences. New Series
review text: A well-known theorem of \textit{J. Tits} [J. Algebra 20, 250-270 (1972; Zbl 0236.20032)] states that a finitely generated linear group over a field either is soluble-by-finite or contains a non-cyclic free subgroup. In this paper the authors prove that this Tits alternative also holds for short generalized tetrahedron groups. Here a group \(G\) defined by a presentation \(G=\langle x,y,z\mid x^l=y^m=z^n=W_1^p(x,y)=W_2^q(y,z)=W_3^r(x,z)=1\rangle\), \(2\leq l,m,n,p,q,r\), where each \(W_i(a,b)\) is a cyclically reduced word involving both \(a\) and \(b\), is called a generalized tetrahedron group. The group \(G\) is a short generalized tetrahedron group if all the \(W_i(a,b)\) have length at most \(4\) in the respective free product on \(a,b\).
reviewed by: Martyn Dixon
description: scientific article; zbMATH DE number 6076257