On the probability of generating a minimal d-generated group

DOI10.1017/S1446788700002822zbMath1011.20025OpenAlexW2132227938MaRDI QIDQ2765549

Fiorenza Morini, Andrea Lucchini, Francesca Dalla Volta

Publication date: 5 March 2003

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446788700002822

zbMATH Keywords

finite groupsnumbers of generatorsminimal generating setsminimal normal subgroups

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Generators, relations, and presentations of groups (20F05) Probabilistic methods in group theory (20P05)

Related Items (10)

A 2-generated just-infinite profinite group which is not positively generated. ⋮ Boundedly generated subgroups of finite groups ⋮ On boundedly generated subgroups of profinite groups. ⋮ Crowns and factorization of the probabilistic zeta function of a finite group. ⋮ Counting irreducible modules for profinite groups ⋮ GENERATING MAXIMAL SUBGROUPS OF FINITE ALMOST SIMPLE GROUPS ⋮ Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements ⋮ The number of maximal subgroups and probabilistic generation of finite groups ⋮ Coprime invariable generation and minimal-exponent groups. ⋮ Bounds on the number of maximal subgroups of finite groups

Cites Work

• Some applications of the first cohomology group
• The probability of generating a finite classical group
• Zu einem von B. H. und H. Neumann gestellten Problem
• Decomposition of the Relation Modules of a Finite Group
• The smallest group with non-zero presentation rank
• On groups withd-generator subgroups of coprime index

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