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

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

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arXiv · 1708.03245

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

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

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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).

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Tushar Kanta Naik, Rahul Dattatraya Kitture, Manoj K. Yadav. 2017-08-10. Finite $p$-Groups of Nilpotency Class $3$ with Two Conjugacy Class Sizes. https://arxiv.org/abs/1708.03245

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