TITLE: Finite subgroups of relatively hyperbolic groups
QUESTION [11 upvotes]: It is well known that in a given $\delta$-hyperbolic group there are only finitely many conjugacy classes of finite subgroups. This is clearly false for relatively hyperbolic groups since we have no control over the parabolic subgroups. Fix a relatively hyperbolic group $\Gamma$ with parabolic subgroups $P_i$. Are there only finitely many conjugacy classes of finite subgroups $F<\Gamma$ with the property that $F$ is contained in a two-ended subgroup $H<\Gamma$ which is not conjugate into any $P_i$? Perhaps weaker: are there only finitely many isomorphism types of two-ended subgroups which are not conjugate into any parabolic? Weaker still: Is there an upper bound to the orders of elements in such subgroups $F$?
(Motivation: I am trying to find a law obeyed by non-parabolic two-ended subgroups of relatively hyperbolic groups, or at least a partition of them into finitely many families, each of which obeys a law.)

REPLY [3 votes]: This question is stated as Corollary 9.6 in Strong accessibility for finitely presented groups but much of the actual proof is in Lemma 9.5.
The proof doesn't quite follow Lee's sketch (which I'm sure works.) I know this is an old question, but I'm providing this answer for completeness and for the cheap thrill of gratuitous self-promotion.