On finite $p$-groups whose central automorphisms are all class preserving

Manoj K. Yadav

On finite $p$-groups whose central automorphisms are all class preserving

Group Theory 2018-07-10 v3

Authors: Manoj K. Yadav

Abstract

We obtain certain results on a finite $p$ -group whose central automorphisms are all class preserving. In particular, we prove that if $G$ is a finite $p$ -group whose central automorphisms are all class preserving, then $d(G)$ is even, where $d(G)$ denotes the number of elements in any minimal generating set for $G$ . As an application of these results, we obtain some results regarding finite $p$ -groups whose automorphisms are all class preserving. In particular, we prove that if $G$ is a finite $p$ -groups whose automorphisms are all class preserving, then order of $G$ is at least $p^8$ and the order of the automorphism group of $G$ is at least $p^12$ .

Keywords

finite groups finite group theory automorphism groups

Cite

@article{arxiv.1208.3046,
  title  = {On finite $p$-groups whose central automorphisms are all class preserving},
  author = {Manoj K. Yadav},
  journal= {arXiv preprint arXiv:1208.3046},
  year   = {2018}
}

Comments

12 pages, Accepted for publication in Comm. Algebra, A minor modification is done in the proof of Proposition 3.4 to make it work for all primes (including 2)

On finite $p$-groups whose central automorphisms are all class preserving

Abstract

Keywords

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