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

Adolfo Ballester-Bolinches, Ramón Esteban-Romero and Paz Jiménez-Seral
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Adolfo Ballester-Bolinches: Departament de Matemàtiques, Universitat de València, Dr. Moliner 50, Burjassot, 46100 València, Spain
Ramón Esteban-Romero: Departament de Matemàtiques, Universitat de València, Dr. Moliner 50, Burjassot, 46100 València, Spain
Paz Jiménez-Seral: Departamento de Matemáticas, Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain

Mathematics, 2022, vol. 10, issue 7, 1-25

Abstract: 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.

Keywords: finite group; maximal subgroup; probabilistic generation; primitive group (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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