The Tits alternative for non-spherical triangles of groups

  • Triangles of groups have been introduced by Gersten and Stallings. They are, roughly speaking, a generalization of the amalgamated free product of two groups and occur in the framework of Corson diagrams. First, we prove an intersection theorem for Corson diagrams. Then, we focus on triangles of groups. It has been shown by Howie and Kopteva that the colimit of a hyperbolic triangle of groups contains a non-abelian free subgroup. We give two natural conditions, each of which ensures that the colimit of a non-spherical triangle of groups either contains a non-abelian free subgroup or is virtually solvable.

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Author:Johannes Cuno, Jörg LehnertGND
Parent Title (German):Transactions of the London Mathematical Society, 2.2015, S. 93–124
Publisher:Oxford Univ. Press
Place of publication:Oxford
Document Type:Article
Year of Completion:2015
Year of first Publication:2015
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2016/02/09
Page Number:32
First Page:93
Last Page:124
(c) 2015 Author(s). This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoCreative Commons - Namensnennung 4.0