Bounds on the Number of Maximal Subgroups of Finite Groups: Applications

被引：2

作者：

Ballester-Bolinches, Adolfo ^{[1
]}

Esteban-Romero, Ramon ^{[1
]}

Jimenez-Seral, Paz ^{[2
]}

机构：

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

[2] Univ Zaragoza, Dept Matemat, Pedro Cerbuna 12, Zaragoza 50009, Spain

来源：

MATHEMATICS | 2022年 / 10卷 / 07期

关键词：

finite group; maximal subgroup; probabilistic generation; primitive group; BASE SIZES; PERMUTATION-GROUPS;

D O I：

10.3390/math10071153

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The determination of bounds for the number of maximal subgroups of a given index in a finite group is relevant to estimate the number of random elements needed to generate a group with a given probability. In this paper, we obtain new bounds for the number of maximal subgroups of a given index in a finite group and we pin-point the universal constants that appear in some results in the literature related to the number of maximal subgroups of a finite group with a given index. This allows us to compare properly our bounds with some of the known bounds.

引用

页数：25

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