Probabilistic generation of finite groups with a unique minimal normal subgroups

DOI10.1112/jlms/jds076zbMath1331.20079OpenAlexW2025633502MaRDI QIDQ2840161

Eloisa Detomi, Andrea Lucchini

Publication date: 17 July 2013

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

Full work available at URL: https://doi.org/10.1112/jlms/jds076

zbMATH Keywords

finite groupsnumbers of generatorsrandom elementsmonolithic groupsminimal generating setsrandom choicesprobabilistic generation

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Generators, relations, and presentations of groups (20F05) Simple groups: alternating groups and groups of Lie type (20D06) Probabilistic methods in group theory (20P05)

Related Items (12)

Generating minimally transitive permutation groups. ⋮ On the length of a finite group and of its 2-generator subgroups ⋮ Genus, thickness and crossing number of graphs encoding the generating properties of finite groups ⋮ On boundedly generated subgroups of profinite groups. ⋮ On the probability of generating a monolithic group. ⋮ FINITE GROUPS WITH INDEPENDENT GENERATING SETS OF ONLY TWO SIZES ⋮ Prefrattini subgroups and crowns ⋮ The minimum generating set problem ⋮ On profinite groups with positive rank gradient ⋮ GENERATING MAXIMAL SUBGROUPS OF FINITE ALMOST SIMPLE GROUPS ⋮ Finite groups with planar generating graph ⋮ Coprime invariable generation and minimal-exponent groups.

Uses Software

• GAP

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