2类的幂零群

IF 0.7 4区数学 Q2 MATHEMATICS

Experimental Mathematics Pub Date : 2021-06-20 DOI:10.1080/10586458.2021.1926003

James Williams

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引用次数: 0

摘要

摘要本文研究了标准幂零类2的幂零群的幂零类。我们概述了利用计算机代数系统GAP收集数据的过程，在此基础上提出了一个猜想，最后证明了这个猜想。特别地，我们证明了对于p为奇素数的2类pn阶幂零群，G的幂零类不超过其整数部分。我们还从群体中强大的阶级的角度来识别和解释这意味着什么。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Powerfully Nilpotent Groups of Class 2

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 . We also identify and explain what this means in terms of the powerful coclass of the group.

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来源期刊

Experimental Mathematics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses. Experiment has always been, and increasingly is, an important method of mathematical discovery. (Gauss declared that his way of arriving at mathematical truths was "through systematic experimentation.") Yet this tends to be concealed by the tradition of presenting only elegant, fully developed, and rigorous results. Experimental Mathematics was founded in the belief that theory and experiment feed on each other, and that the mathematical community stands to benefit from a more complete exposure to the experimental process. The early sharing of insights increases the possibility that they will lead to theorems: An interesting conjecture is often formulated by a researcher who lacks the techniques to formalize a proof, while those who have the techniques at their fingertips have been looking elsewhere. Even when the person who had the initial insight goes on to find a proof, a discussion of the heuristic process can be of help, or at least of interest, to other researchers. There is value not only in the discovery itself, but also in the road that leads to it.