极大子群的个数与有限群的概率生成

IF 0.7 Q2 MATHEMATICS

International Journal of Group Theory Pub Date : 2020-03-01 DOI:10.22108/IJGT.2019.114469.1521

Adolfo Ballester Bolinches, R. Esteban-Romero, P. Jiménez-Seral, H. Meng

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引用次数: 0

摘要

在这个研究中，我们给出了有限群的给定索引的极大子群数目的一些有意义的界。作为一个结果，生成具有高概率的有限d生成群所需的随机生成数的新边界明显严格于Jaikin-Zapirain和Pyber的论文(有限群和无限群的随机生成和群枚举)中得到的边界。数学。}，} textbf{183}(2011) 769—814)。Jaikin-Zapirain和Pyber的结果，以及Lubotzky、Detomi和Lucchini的其他结果，作为我们的定理的特殊情况出现。

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The number of maximal subgroups and probabilistic generation of finite groups

In this survey we present some significant bounds for the‎ ‎number of maximal subgroups of a given index of a finite group‎. ‎As a‎ ‎consequence‎, ‎new bounds for the number of random‎ ‎generators needed to generate a finite $d$-generated group with high‎ ‎probability which are significantly tighter than the ones obtained in‎ ‎the paper of Jaikin-Zapirain and Pyber (Random generation of finite‎ ‎and profinite groups and group enumeration‎, ‎emph{Ann. Math.}‎, ‎textbf{183} (2011) 769--814) are obtained‎. ‎The results of‎ ‎Jaikin-Zapirain and Pyber‎, ‎as well as other results of Lubotzky‎, ‎Detomi‎, ‎and Lucchini‎, ‎appear as particular cases of our theorems‎.

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来源期刊

International Journal of Group Theory MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

30 weeks

期刊介绍： International Journal of Group Theory (IJGT) is an international mathematical journal founded in 2011. IJGT carries original research articles in the field of group theory, a branch of algebra. IJGT aims to reflect the latest developments in group theory and promote international academic exchanges.