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On finite p-groups whose automorphisms are all central

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Abstract

An automorphism α of a group G is said to be central if α commutes with every inner automorphism of G. We construct a family of non-special finite p-groups having abelian automorphism groups. These groups provide counterexamples to a conjecture of A. Mahalanobis [Israel J. Math. 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, pp. 111–127].

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Authors and Affiliations

  1. Department of Mathematics, Central University of Bihar, Patna, India

    Vivek K. Jain

  2. School of Mathematics, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad, 211019, India

    Manoj K. Yadav

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  1. Vivek K. Jain
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  2. Manoj K. Yadav
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Correspondence to Vivek K. Jain.

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Jain, V.K., Yadav, M.K. On finite p-groups whose automorphisms are all central. Isr. J. Math. 189, 225–236 (2012). https://doi.org/10.1007/s11856-011-0167-5

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  • DOI: https://doi.org/10.1007/s11856-011-0167-5

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