The number of maximal subgroups and probabilistic generation of finite groups
Resumen: 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.
Idioma: Inglés
DOI: 10.22108/ijgt.2019.114469.1521
Año: 2020
Publicado en: International Journal of Group Theory 9, 1 (2020), 31-42
ISSN: 2251-7669

Factor impacto SCIMAGO:

Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2014-54707-C3-1-P
Tipo y forma: Article (Published version)
Área (Departamento): Área Algebra (Dpto. Matemáticas)

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