Resumen: In this paper we obtain significant bounds for the number of maximal subgroups of a given index of a finite group. These results allow us to give new bounds for the number of random generators needed to generate a finite d-generated group with high probability. Idioma: Inglés DOI: 10.1007/s00025-022-01806-1 Año: 2023 Publicado en: Results in Mathematics 78, 1 (2023), 35 [17 pp.] ISSN: 1422-6383 Factor impacto JCR: 1.1 (2023) Categ. JCR: MATHEMATICS rank: 98 / 490 = 0.2 (2023) - Q1 - T1 Categ. JCR: MATHEMATICS, APPLIED rank: 163 / 332 = 0.491 (2023) - Q2 - T2 Factor impacto CITESCORE: 1.9 - Mathematics (miscellaneous) (Q2) - Applied Mathematics (Q3)