2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/109042We prove that if a Cartesian product of alternating groups is topologically finitely generated, then it is the profinite completion of a finitely generated residually finite group. The same holds for Cartesian producs of other simple groups under some natural restrictions.latex 13 pagesGroup TheoryRings and Algebrastext