Presenting parabolic subgroups

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.

15 pages

References in corpus (1)

• Relative hyperbolicity and relative quasiconvexity for countable groups

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