  We 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.
