2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231177We prove that rationally essential manifolds with suitably large fundamental groups do not admit any maps of non-zero degree from products of closed manifolds of positive dimension. Particular examples include all manifolds of non-positive sectional curvature of rank one and all irreducible locally symmetric spaces of non-compact type. For closed manifolds from certain classes, say non-positively curved ones, or certain surface bundles over surfaces, we show that they do admit maps of non-zero degree from non-trivial products if and only if they are virtually diffeomorphic to products.22 pages; updated references and corrected a typo; to appear in the Journal of the London Mathematical SocietyGeometric TopologyDifferential GeometryGroup Theory53C23 (Primary); 20F34, 20F67, 57N65 (Secondary)text