2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145525We examine the selective screenability property in topological groups. In the metrizable case we also give characterizations in terms of the Haver property and finitary Haver property respectively relative to left-invariant metrics. We prove theorems stating conditions under which the properties are preserved by products. Among metrizable groups we characterize the ones of countable covering dimension by a natural game.12 pages. Improved Theorem 5. Added remarks. Fixed typographical errorsGeneral TopologyGroup Theory54D20, 54D45, 55M10, 03E20text