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

Mathematics

Adolfo Ballester-Bolinches¹  Ramón Esteban-Romero¹  Paz Jiménez-Seral² 

[1] Departament de Matemàtiques, Universitat de València, Dr. Moliner 50, Burjassot, 46100 València, Spain;Departamento de Matemáticas, Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain;

关键词: finite group;    maximal subgroup;    probabilistic generation;    primitive group;   

DOI  :  10.3390/math10071153

来源: DOAJ

【 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.

【 授权许可】

Unknown