On p-groups of maximal class

2020/06/28 by Snanou, Noureddine
#20D15 #FOS: Mathematics #G.2.m #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2006.15737

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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