2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169077We use wreath products to provide criteria for a group to be conjugacy separable or omnipotent. These criteria are in terms of virtual retractions onto cyclic subgroups. We give two applications: a straightforward topological proof of the theorem of Stebe that infinite-order elements of Fuchsian groups (of the first type) are conjugacy distinguished, and a proof that surface groups are omnipotent.18 pagesGroup TheoryGeometric Topology20E26; 57N05text