The number of maximal subgroups and probabilistic generation of finite groups

Ballester-Bolinches, AdolfoEsteban Romero, RamónJiménez-Seral, PazMeng, Hangyang2021-07-202021-07-202020-032251-7650https://riunet.upv.es/handle/10251/169538[EN] 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.Reconocimiento (by)Finite groupMaximal subgroupProbabilistic generationPrimitive groupMATEMATICA APLICADAThe number of maximal subgroups and probabilistic generation of finite groupsArtículo10.22108/ijgt.2019.114469.1521Abierto