Abstract

In this article, we investigate the powerful nilpotency class of powerfully nilpotent groups of standard nilpotency class 2. We outline the process of collecting data using the computer algebra system GAP, formulating a conjecture based on the data, and finally we prove the conjecture. In particular, we prove that for a powerfully nilpotent group of nilpotency class 2 and order pⁿ, where p is an odd prime, the powerful nilpotency class of G is at most the integer part of $n/2$. We also identify and explain what this means in terms of the powerful coclass of the group.

中文翻译：

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第 2 类的幂幂群

摘要

在这篇文章中，我们研究了标准幂零类2的幂幂群的幂幂幂类。我们概述了使用计算机代数系统GAP收集数据的过程，并根据数据提出了一个猜想，最后证明了这个猜想。特别是，我们证明对于幂零类 2 和阶p ⁿ的幂幂群，其中p是奇素数， G的幂幂类至多是整数部分$n/\mathrm{2个}$. 我们还根据组的强大 coclass来识别和解释这意味着什么。