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arXiv · 2006.15737

On p-groups of maximal class

Noureddine Snanou
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Abstract

Recall that a $p$-group of order $p^ {n} >p^ {3} $ is of maximal class, if its nilpotency class is $n-1$. In this paper, we study the $p$-groups of maximal class. Furthermore, we introduce a subgroup of a $p$-group of maximal class called the fundamental subgroup. This group plays a fundamental role in the development of the general theory of $p$-groups of maximal class. As an application, we study some special class of finite $p$-groups of maximal class and exponent $p$.

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Noureddine Snanou. 2022-10-04. On p-groups of maximal class. https://arxiv.org/abs/2006.15737

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