2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111651We discuss the possibility of lifting finite subgroups, and in particular finite cyclic subgroups, with respect to the canonical projections between automorphism and outer automorphism groups of free groups, surface groups and their abelianizations.Geometric TopologyGroup Theory57M99; 20F65Lifting finite groups of outer automorphisms of free groups, surface groups and their abelianizationstext