Tree groups and the 4-string pure braid group
type: Item
instance of: scholarly article
title: Tree groups and the 4-string pure braid group
zbMATH Open document ID: 0727.20019
DOI: 10.1016/0022-4049(91)90072-A
author: Carl Droms
author: Jacques Lewin
author: Herman J. Servatius
published in: Journal of Pure and Applied Algebra
publication date: 1991-01-01T00:00:00Z
review text: It is shown that the (unperturbed) braid group on four strings \(B_ 4\) is an HNN-extension of the graph group \(F_ 5\) of a certain graph S having 5 vertices and 5 edges. As a consequence, a conjecture due to J. Tits, referring to the structure of a suitable subgroup of the braid group, is resolved for the special case \(B_ 4\). Various other results are obtained dealing for example with the question of the linearity of the braid groups.
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 20E08
zbMATH DE Number: 4200472
zbMATH Keywords: HNN-extension
zbMATH Keywords: graph group
zbMATH Keywords: braid groups
reviewed by: J. Huebschmann
MaRDI profile type: Publication
cites work: Artin groups and infinite Coxeter groups
cites work: Subgroups of Direct Products of Free Groups
cites work: Aspherical group presentations
cites work: An exact sequence for rings of polynomials in partly commuting indeterminates
cites work: Graph groups, coherence, and three-manifolds
cites work: Isomorphisms of Graph Groups
cites work: Subgroups of graph groups
cites work: THE BRAID GROUP AND OTHER GROUPS
cites work: Q4135772
cites work: Automorphisms of graph groups.
cites work: Generalized Free Products of Linear Groups
description: scientific article; zbMATH DE number 4200472