89268 20230914083250.0 doi 10.22108/ijgt.2019.114469.1521 sideral 117524 ART-2020-117524 eng Ballester-Bolinches, Adolfo The number of maximal subgroups and probabilistic generation of finite groups 2020 Access copy available to the general public Unrestricted 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. info:eu-repo/grantAgreement/ES/MINECO/MTM2014-54707-C3-1-P info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 0.383 2020 Algebra and Number Theory 2020 Q3 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Esteban-Romero, Ramón Jimenez-Seral, Paz Universidad de Zaragoza (orcid)0000-0003-4809-1784 Meng, Hangyang 2006 005 Universidad de Zaragoza Dpto. Matemáticas Área Algebra 9, 1 (2020), 31-42 International Journal of Group Theory 2251-7669 233730 http://zaguan.unizar.es/record/89268/files/texto_completo.pdf Versión publicada 40991 http://zaguan.unizar.es/record/89268/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:89268 articulos driver 2023-09-13-10:50:56 ARTICLE