THE NUMBER OF MAXIMAL SUBGROUPS AND PROBABILISTIC GENERATION OF FINITE GROUPS

被引：0

作者：

Ballester-Bolinches, Adolfo ^{[1
]}

Esteban-Romero, Ramon ^{[1
,2
]}

Jimenez-Seral, Paz ^{[3
]}

Meng, Hangyang ^{[1
]}

机构：

[1] Univ Valencia, Dept Matemat, Dr Moliner 50, E-46100 Valencia, Spain

[2] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Cami Vera S-N, E-46022 Valencia, Spain

[3] Univ Zaragoza, Dept Matemat, Pedro Cerbuna 12, E-50009 Zaragoza, Spain

来源：

INTERNATIONAL JOURNAL OF GROUP THEORY | 2020年 / 9卷 / 01期

关键词：

Finite group; maximal subgroup; probabilistic generation; primitive group; PROFINITE GROUPS; CROWNS;

D O I：

10.22108/ijgt.2019.114469.1521

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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, Ann. Math., 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.

引用

页码：31 / 42

页数：12

共 22 条

[1]

Baer R., 1957, ILLINOIS J MATH, V1, P115, DOI 10.1215/ijm/1255379396

[2]

Ballester-Bolinches A., 2006, MATH ITS APPL, V584, DOI [10.1007/1-4020-4719-3, DOI 10.1007/1-4020-4719-3]

[3]

Ballester-Bolinches A., PREPRINT

[4] Maximal subgroups in finite and profinite groups [J].