2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99419We prove that all elements of infinite order in $Out(F_n)$ have positive translation lengths; moreover, they are bounded away from zero. Consequences include a new proof that solvable subgroups of $Out(F_n)$ are finitely generated and virtually abelian and the new result that such subgroups are quasi-convex.Corrected typosGroup TheoryGeometric Topology57M07, 20F28text