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arXiv · 2002.02694

Powerfully nilpotent groups of rank 2 or small order

Gunnar Traustason·James Williams
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Abstract

In this paper we continue the study of powerfully nilpotent groups. These are powerful $p$-groups possessing a central series of a special kind. To each such group one can attach a powerful nilpotency class that leads naturally to the notion of a powerful coclass and classification in terms of an ancestry tree. In this paper we will give a full classification of powerfully nilpotent groups of rank $2$. The classification will then be used to arrive at a precise formula for the number of powerfully nilpotent groups of rank $2$ and order $p^{n}$. We will also give a detailed analysis of the ancestry tree for these groups. The second part of the paper is then devoted to a full classification of powerfully nilpotent groups of order up to $p^{6}$.

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Gunnar Traustason, James Williams. 2020-02-07. Powerfully nilpotent groups of rank 2 or small order. https://arxiv.org/abs/2002.02694

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