Rendiconti del Seminario Matematico della Università di Padova


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Volume 120, 2008, pp. 73–77
DOI: 10.4171/RSMUP/120-5

Automorphisms Fixing Every Normal Subgroup of a Nilpotent-by-Abelian Group

Gérard Endimioni[1]

(1) Université de Provence, Marseille, France

Among other things, we prove that the group of automorphisms fixing every normal subgroup of a (nilpotent of class c)-by-abelian group is (nilpotent of class ≤ c)-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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Endimioni Gérard: Automorphisms Fixing Every Normal Subgroup of a Nilpotent-by-Abelian Group. Rend. Sem. Mat. Univ. Padova 120 (2008), 73-77. doi: 10.4171/RSMUP/120-5