doi:10.22108/ijgt.2019.114469.1521engBallester-Bolinches, AdolfoEsteban-Romero, RamónJimenez-Seral, PazMeng, HangyangThe number of maximal subgroups and probabilistic generation of finite groupsART-2020-117524In 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.2020http://zaguan.unizar.es/record/8926810.22108/ijgt.2019.114469.1521http://zaguan.unizar.es/record/89268oai:zaguan.unizar.es:89268info:eu-repo/grantAgreement/ES/MINECO/MTM2014-54707-C3-1-PInternational Journal of Group Theory 9, 1 (2020), 31-42byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess