#### Volume 13, issue 6 (2013)

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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
Primary: 20F67
Secondary: 20F10
##### 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/