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

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

2007-06-04

arxiv.org/abs/0706.0408v1

Mathematics

Group Theory

6 pages

Scientific paper

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.

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