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The number of maximal subgroups and probabilistic generation of finite groups | ||
| International Journal of Group Theory | ||
| مقاله 5، دوره 9، شماره 1، خرداد 2020، صفحه 31-42 اصل مقاله (218.11 K) | ||
| نوع مقاله: Ischia Group Theory 2018 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2019.114469.1521 | ||
| نویسندگان | ||
| Adolfo Ballester Bolinches1؛ Ramón Esteban-Romero* 1؛ Paz Jiménez-Seral2؛ Hangyang Meng1 | ||
| 1Departament de Matematiques, Universitat de Valencia, Spain | ||
| 2Departamento de Matematicas, Universidad de Zaragoza, Pedro Cerbuna, Spain | ||
| چکیده | ||
| 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{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. | ||
| کلیدواژهها | ||
| Finite group؛ maximal subgroup؛ probabilistic generation؛ primitive group | ||
| مراجع | ||
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