2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65575We provide a Hilbert-Mumford Criterion for actions of reductive groups $G$ on $Q$-factorial complex varieties. The result allows to construct open subsets admitting a good quotient by $G$ from certain maximal open subsets admitting a good quotient by a maximal torus of $G$. As an application, we show how to obtain all invariant open subsets with good quotient for a given $G$-action on a complete $Q$-factorial toric variety.8 pages, minor changes, to appear in Ann. Inst. FourierAlgebraic Geometry14L24, 14L30text