Presenting parabolic subgroups

Dahmani, François; Guirardel, Vincent

doi:10.2140/agt.2013.13.3203

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Presenting parabolic subgroups

François Dahmani and Vincent Guirardel

Algebraic & Geometric Topology 13 (2013) 3203–3222

DOI: 10.2140/agt.2013.13.3203

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/

Volume 13, issue 6 (2013)