Class-preserving automorphisms of some finite $p$-groups

Mahak Sharma; Deepak Gumber

Class-preserving automorphisms of some finite $p$-groups

Group Theory 2014-07-23 v1

Authors: Mahak Sharma , Deepak Gumber

Abstract

Let $G$ be a finite $p$ -group of order $p^5$ , where $p$ is a prime. We give necessary and sufficient conditions on $G$ such that $G$ has a non-inner class-preserving automorphism. As a consequence, we give short and alternate proofs of results of section 5 of Yadav [Proc. Indian Acad. Sci. (Math. Sci.) 118 (2008), 1-11] and Theorem 4.2 of Kalra and Gumber [Indian J. Pure Appl. Math. 44 (2013), 711-725].

Keywords

finite groups automorphism groups group theory

Cite

@article{arxiv.1407.5921,
  title  = {Class-preserving automorphisms of some finite $p$-groups},
  author = {Mahak Sharma and Deepak Gumber},
  journal= {arXiv preprint arXiv:1407.5921},
  year   = {2014}
}

Comments

To appear in Proc. Indian Acad. Sci

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