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Information Journal Paper

Title

THE NUMBER OF MAXIMAL SUBGROUPS AND PROBABILISTIC GENERATION OF FINITE GROUPS

Pages

  31-42

Abstract

 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.

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    APA: Copy

    BALLESTER BOLINCHES, ADOLFO, Esteban Romero, Ramon, Jimenez Seral, Paz, & Meng, Hangyang. (2020). THE NUMBER OF MAXIMAL SUBGROUPS AND PROBABILISTIC GENERATION OF FINITE GROUPS. INTERNATIONAL JOURNAL OF GROUP THEORY, 9(1), 31-42. SID. https://sid.ir/paper/730830/en

    Vancouver: Copy

    BALLESTER BOLINCHES ADOLFO, Esteban Romero Ramon, Jimenez Seral Paz, Meng Hangyang. THE NUMBER OF MAXIMAL SUBGROUPS AND PROBABILISTIC GENERATION OF FINITE GROUPS. INTERNATIONAL JOURNAL OF GROUP THEORY[Internet]. 2020;9(1):31-42. Available from: https://sid.ir/paper/730830/en

    IEEE: Copy

    ADOLFO BALLESTER BOLINCHES, Ramon Esteban Romero, Paz Jimenez Seral, and Hangyang Meng, “THE NUMBER OF MAXIMAL SUBGROUPS AND PROBABILISTIC GENERATION OF FINITE GROUPS,” INTERNATIONAL JOURNAL OF GROUP THEORY, vol. 9, no. 1, pp. 31–42, 2020, [Online]. Available: https://sid.ir/paper/730830/en

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