Finite $p$-Groups of Nilpotency Class $3$ with Two Conjugacy Class Sizes

Tushar Kanta Naik; Rahul Dattatraya Kitture; Manoj K. Yadav

Finite $p$-Groups of Nilpotency Class $3$ with Two Conjugacy Class Sizes

Group Theory 2017-08-15 v2

Authors: Tushar Kanta Naik , Rahul Dattatraya Kitture , Manoj K. Yadav

Abstract

It is proved that, for a prime $p>2$ and integer $n\geq 1$ , finite $p$ -groups of nilpotency class $3$ and having only two conjugacy class sizes $1$ and $p^n$ exist if and only if $n$ is even; moreover, for a given even positive integer, such a group is unique up to isoclinism (in the sense of Philip Hall).

Keywords

finite groups conjugacy classes in groups finite group theory

Cite

@article{arxiv.1708.03245,
  title  = {Finite $p$-Groups of Nilpotency Class $3$ with Two Conjugacy Class Sizes},
  author = {Tushar Kanta Naik and Rahul Dattatraya Kitture and Manoj K. Yadav},
  journal= {arXiv preprint arXiv:1708.03245},
  year   = {2017}
}

Comments

24 pages, Commets are welcome, some anomalies in the first version have been corrected

Finite $p$-Groups of Nilpotency Class $3$ with Two Conjugacy Class Sizes

Abstract

Keywords

Cite

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