2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78598We prove that an automorphism $ϕ:F\to F$ of a finitely generated free group $F$ is hyperbolic in the sense of Gromov if it has no nontrivial periodic conjugacy classes.22 pages Revised according to referee's suggestions, added some detailsGroup Theorytext