The Nilpotent Probability of Finite Groups

IF 0.8 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2025-04-15 DOI:10.1007/s10114-025-2510-5

Huaquan Wei, Xuanyou Hou, Changman Sun, Xixi Diao, Hui Wu, Liying Yang

引用次数: 0

Abstract

Let G be a finite group. We denote by ν(G) the probability that two randomly chosen elements of G generate a nilpotent subgroup. In this paper, we characterize the structure of finite groups G with lower bounds \({1 \over p}, \, {{p^{2}+8} \over {9p^{2}}}\) and \({p+3} \over {4p}\) on ν(G), where p is a prime divisor of ∣G∣.

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有限群的幂零概率

设G是一个有限群。我们用ν(G)表示G中随机选择的两个元素产生一个幂零子群的概率。本文刻画了ν(G)上具有下界\({1 \over p}, \, {{p^{2}+8} \over {9p^{2}}}\)和\({p+3} \over {4p}\)的有限群G的结构，其中p是∣G∣的素数因子。

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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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.