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Presenting parabolic
subgroups
François Dahmani and Vincent Guirardel |
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Algebraic & Geometric Topology 13 (2013) 3203–3222
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Abstract |
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Consider a relatively hyperbolic group . We prove that if is finitely presented, so are its parabolic subgroups. Moreover, a presentation of the parabolic subgroups can be found algorithmically from a presentation of , 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
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Mathematical Subject Classification 2010
Primary: 20F67
Secondary: 20F10
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References |
Publication
Received: 3 October 2011
Revised: 5 October 2012
Accepted: 15 March 2013
Published: 12 September 2013
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Authors |
| François Dahmani | |
| Institut Fourier Université de Grenoble 1 100 rue des Maths, BP 76 38402 St. Martin d’Hères Cedex France |
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| 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 |
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| http://perso.univ-rennes1.fr/vincent.guirardel/ | |
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