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

2007/06/04 by G. Endimioni, Endimioni, G.
Mathematics · #20E36 #20F16 #20F28 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.0706.0408

openalex publication_date 2007/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Normal automorphisms of a free metabelian nilpotent group

Related

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• On the polynomial automorphisms of a group
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• An Automorphism of A Free Metabelian Group Without Fixed Points
• Groups in which every non-nilpotent subgroup is self-normalizing