2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101195We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable hyperbolic group is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated Fuchsian group and of every free-by-finite group is resudually finite. We also generalize the main result for relatively hyperbolic groups.12 pages, an addendum is added that generalizes the reults for relatively hyperbolic groupsGroup TheoryGeometric Topology20E05; 57A05; 20E07; 20E08; 57M60text