Presenting parabolic subgroups

François Dahmani (1, 2) , Vincent Guirardel (3)

1 IF - Institut Fourier
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: relatively hyperbolic groups; finite presentations; van Kampen diagrams; decision problems

Domaines: Théorie des groupes [math.GR]; Topologie géométrique [math.GT]

François Dahmani, Vincent Guirardel. Presenting parabolic subgroups. Algebraic and Geometric Topology, 2013, 13, pp.3203-3222. ⟨10.2140/agt.2013.13.3203⟩. ⟨hal-00560910⟩