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 $\{H_λ\}_{λ\in Λ}$. Suppose that $G$ is given by a finite relative presentation $\mathcal{P}$ 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 $\mathcal{P}$. This upper bound is computable if $G$ is finitely generated and the word problem in each $H_λ$, $λ\in Λ$, is decidable.