2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129802Among other things, we prove that the group of automorphisms fixing every normal subgroup of a nilpotent-by-abelian group is nilpotent-by-metabelian. In particular, the group of automorphisms fixing every normal subgroup of a metabelian group is soluble of derived length at most 3. An example shows that this bound cannot be improved.6 pagesGroup Theory20E36, 20F16, 20F28text