Automorphisms fixing every normal subgroup of a nilpotent-by-abelian group

Abstract

Among 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 pages

References in corpus (1)

• Normal automorphisms of a free metabelian nilpotent group