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Tits alternatives for graph products

Tits alternatives for graph products
Tits alternatives for graph products
We discuss various types of Tits Alternative for subgroups of graph products of groups, and prove that, under some natural conditions, a graph product of groups satisfies a given form of Tits Alternative if and only if each vertex group satisfies this alternative. As a corollary, we show that every finitely generated subgroup of a graph product of virtually solvable groups is either virtually solvable or large. As another corollary, we prove that every non-abelian subgroup of a right angled Artin group has an epimorphism onto the free group of rank 2. In the course of the paper we develop the theory of parabolic subgroups, which allows to describe the structure of subgroups of graph products that contain no non-abelian free subgroups. We also obtain a number of results regarding the stability of some group properties under taking graph products.
graph products, tits alternative, right angled coxeter groups, right angled artin groups, graph groups
55-83
Antolin, Yago
2ff7c13c-8a0d-4a50-9de5-63a750896e4c
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Antolin, Yago
2ff7c13c-8a0d-4a50-9de5-63a750896e4c
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d

Antolin, Yago and Minasyan, Ashot (2015) Tits alternatives for graph products. Journal für die reine und angewandte Mathematik, 704, 55-83. (doi:10.1515/crelle-2013-0062).

Record type: Article

Abstract

We discuss various types of Tits Alternative for subgroups of graph products of groups, and prove that, under some natural conditions, a graph product of groups satisfies a given form of Tits Alternative if and only if each vertex group satisfies this alternative. As a corollary, we show that every finitely generated subgroup of a graph product of virtually solvable groups is either virtually solvable or large. As another corollary, we prove that every non-abelian subgroup of a right angled Artin group has an epimorphism onto the free group of rank 2. In the course of the paper we develop the theory of parabolic subgroups, which allows to describe the structure of subgroups of graph products that contain no non-abelian free subgroups. We also obtain a number of results regarding the stability of some group properties under taking graph products.

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e-pub ahead of print date: 23 July 2013
Published date: July 2015
Keywords: graph products, tits alternative, right angled coxeter groups, right angled artin groups, graph groups
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 338953
URI: https://eprints.soton.ac.uk/id/eprint/338953
PURE UUID: 3c5f32c3-61ee-475a-a840-8688b4abb2db
ORCID for Ashot Minasyan: ORCID iD orcid.org/0000-0002-4986-2352

Catalogue record

Date deposited: 21 May 2012 10:48
Last modified: 20 Jul 2019 00:51

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Contributors

Author: Yago Antolin
Author: Ashot Minasyan ORCID iD

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