On finite p-groups whose automorphisms are all central |
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Authors: | Vivek K. Jain Manoj K. Yadav |
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Affiliation: | 1.Department of Mathematics,Central University of Bihar,Patna,India;2.School of Mathematics,Harish-Chandra Research Institute,Jhunsi,India |
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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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