Normal automorphisms of a free metabelian nilpotent group
An automorphism of a group is said to be normal if it preserves each normal subgroup. In this paper, we determine the normal automorphisms of a free metabelian nilpotent group.
math.GR↗
arXiv subjects
G. Endimioni
Publications and source records attributed to G. Endimioni.
Automorphisms fixing every normal subgroup of a nilpotent-by-abelian group
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.
math.GR↗
On the polynomial automorphisms of a group
We prove that if a group is nilpotent (resp. metabelian), then so is the subgroup of its automorphism group generated by all polynomial automorphisms.
math.GR↗
On the Group of Polynomial Functions in a Group
In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.
math.GR↗