On finite $p$-groups whose automorphisms are all central

Details On finite $p$-groups whose automorphisms are all central On finite $p$-groups whose automorphisms are all central

2010-05-12

arxiv.org/abs/1005.2066v2

Israel J. Math. xxx (2012), 1-12

Mathematics

Group Theory

11 pages, Counter examples to a conjecture from [Israel J. Math., {\bf 165} (2008), 161 - 187]; This paper will appear in Isra

Scientific paper

10.1007/s11856-011-0167-5

An automorphism $\alpha$ of a group $G$ is said to be central if $\alpha$ commutes with every inner automorphism of $G$. We construct a family of non-special finite $p$-groups having abelian automorphism groups. These groups provide counter examples to a conjecture of A. Mahalanobis [Israel J. Math., {\bf 165} (2008), 161 - 187]. We also construct a family of finite $p$-groups having non-abelian automorphism groups and all automorphisms central. This solves a problem of I. Malinowska [Advances in group theory, Aracne Editrice, Rome 2002, 111-127].

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