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

Source: [On finite $p$-groups whose automorphisms are all central](<https://www.sota2.com/research/paper/68fa4fda1e209131ce96694a>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:31:40.210Z

Authors: Vivek K. Jain, Manoj K. Yadav

Published: 2010-05-12T12:18:12.000Z

## Abstract

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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1005.2066>)

[PDF](<https://arxiv.org/pdf/1005.2066.pdf>)