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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Adolfo Ballester-Bolinches & Ramón Esteban-Romero & Paz Jiménez-Seral, 2022. "Bounds on the Number of Maximal Subgroups of Finite Groups: Applications," Mathematics, MDPI, vol. 10(7), pages 1-25, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1153-:d:786147
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