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Title

The number of maximal subgroups and probabilistic generation of‎ ‎finite groups

Year: 1399
COI: JR_THEGR-9-1_005
Language: EnglishView: 31
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Authors

Adolfo Ballester Bolinches - Departament de Matematiques‎, ‎Universitat de Valencia‎, ‎Spain
Ramón Esteban-Romero - Departament de Matematiques‎, ‎Universitat de Valencia‎, ‎Spain
Paz Jiménez-Seral - Departamento de Matematicas‎, ‎Universidad de Zaragoza‎, ‎Pedro Cerbuna‎, Spain
Hangyang Meng - Departament de Matematiques‎, ‎Universitat de Valencia‎, ‎Spain

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, ‎\emph{Ann.\ Math.}‎, ‎\textbf{۱۸۳} (۲۰۱۱) ۷۶۹--۸۱۴) 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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Paper COI Code

This Paper COI Code is JR_THEGR-9-1_005. Also You can use the following address to link to this article. This link is permanent and is used as an article registration confirmation in the Civilica reference:

https://civilica.com/doc/1194939/

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Ballester Bolinches, Adolfo and Esteban-Romero, Ramón and Jiménez-Seral, Paz and Meng, Hangyang,1399,The number of maximal subgroups and probabilistic generation of‎ ‎finite groups,https://civilica.com/doc/1194939

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