The number of maximal subgroups and probabilistic generation of finite groups

Ballester-Bolinches, Adolfo ; Esteban-Romero, Ramón ; Jimenez-Seral, Paz (Universidad de Zaragoza) ; Meng, Hangyang

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: 0.383 - Algebra and Number Theory (Q3)

Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2014-54707-C3-1-P

Tipo y forma: Article (Published version)

Área (Departamento): Área Algebra (Dpto. Matemáticas)