#### 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