2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63933We construct examples of two-step and three-step nilpotent Lie groups whose automorphism groups are `small' in the sense of either not having a dense orbit for the action on the Lie group, or being nilpotent (the latter being stronger). From the results we get also new examples of compact manifolds covered by two-step simply connected Lie groups, which do not admit Anosov automorphisms.14 pagesDynamical Systems22D45; 22E25text