Finite non-parabolic subgroups of relatively hyperbolic groups

Abstract

Let G be a group that is relatively hyperbolic with respect to a collection of subgroups ${\left\{H_{\lambda }\right\}}_{\lambda \in \Lambda }$. Suppose that G is given by a finite relative presentation $P$ with respect to this collection. We give an upper bound on the orders of finite non-parabolic subgroups of G in terms of some fundamental constants associated with $P$. This upper bound is computable if G is finitely generated and the word problem in each $H_{\lambda }$, $\lambda \in \Lambda$, is decidable.