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Presenting parabolic subgroups

François Dahmani and Vincent Guirardel

Algebraic & Geometric Topology 13 (2013) 3203–3222
Abstract

Consider a relatively hyperbolic group G. We prove that if G is finitely presented, so are its parabolic subgroups. Moreover, a presentation of the parabolic subgroups can be found algorithmically from a presentation of G, a solution of its word problem and generating sets of the parabolic subgroups. We also give an algorithm that finds parabolic subgroups in a given recursively enumerable class of groups.

Keywords
relatively hyperbolic groups, finite presentations, van Kampen diagrams, decision problems
Mathematical Subject Classification 2010
Primary: 20F67
Secondary: 20F10
References
Publication
Received: 3 October 2011
Revised: 5 October 2012
Accepted: 15 March 2013
Published: 12 September 2013
Authors
François Dahmani
Institut Fourier
Université de Grenoble 1
100 rue des Maths, BP 76
38402 St. Martin d’Hères Cedex
France
http://www-fourier.ujf-grenoble.fr/~dahmani/
Vincent Guirardel
Institut de recherche en mathématiques de Rennes
Université de Rennes 1
263 avenue du Général Leclerc
CS 74205
35042 Rennes Cedex
France
http://perso.univ-rennes1.fr/vincent.guirardel/