PUB - Publikationen an der Universität Bielefeld

Suppose that a finitely generated group G is hyperbolic relative to a collection of subgroups P = {P-1,...,P-m}. Let H-1, H-2 be subgroups of G such that H-1 is relatively quasiconvex with respect to P and H-2 is not parabolic. Suppose that H-2 is elementwise conjugate into H-1. Then there exists a finite index subgroup of H-2 which is conjugate into H-1. The minimal length of the conjugator can be estimated. In the case, where G is a limit group, it is sufficient to assume only that H-1 is a finitely generated and H-2 is an arbitrary subgroup of G.