Boundedly generated subgroups of finite groups

DOI10.1515/form.2011.092zbMath1258.20026OpenAlexW2314640013MaRDI QIDQ2905099

Andrea Lucchini, Marta Morigi, P. V. Shumyatskij

Publication date: 24 August 2012

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/form.2011.092

zbMATH Keywords

soluble groupsfinite groupsgeneratorsexponentscomposition factorsspectra2-generator subgroupsprime graphs

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Generators, relations, and presentations of groups (20F05)

Related Items (10)

On the length of a finite group and of its 2-generator subgroups ⋮ On boundedly generated subgroups of profinite groups. ⋮ Prefrattini subgroups and crowns ⋮ Generation of a finite group with Hall maximal subgroups by a pair of conjugate elements. ⋮ Finite groups with arithmetic restrictions on maximal subgroups. ⋮ Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements ⋮ A reduction theorem for nonsolvable finite groups ⋮ ON THE PRIME GRAPH OF SIMPLE GROUPS ⋮ Coprime invariable generation and minimal-exponent groups. ⋮ Exponent preserving subgroups of the finite simple groups

Cites Work

• Some applications of the first cohomology group
• The presentation rank of a direct product of finite groups
• Generators and minimal normal subgroups
• Finite groups in which every two elements generate a soluble subgroup
• Generation of almost simple groups
• On the probability of generating a minimal d-generated group
• On the Fitting height of a finite group
• On groups withd-generator subgroups of coprime index
• Nonsolvable finite groups all of whose local subgroups are solvable

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