On finite $p$-groups whose automorphisms are all central
Group Theory
2012-08-16 v2
Abstract
An automorphism of a group is said to be central if commutes with every inner automorphism of . We construct a family of non-special finite -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 -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].
Keywords
Cite
@article{arxiv.1005.2066,
title = {On finite $p$-groups whose automorphisms are all central},
author = {Vivek K. Jain and Manoj K. Yadav},
journal= {arXiv preprint arXiv:1005.2066},
year = {2012}
}
Comments
11 pages, Counter examples to a conjecture from [Israel J. Math., {\bf 165} (2008), 161 - 187]; This paper will appear in Israel J. Math. in 2012