Recognizing the prime divisors of the index of a proper subgroup.

DOI10.1016/j.jalgebra.2011.02.041zbMath1254.20022OpenAlexW2079536448MaRDI QIDQ657991

Andrea Lucchini, Marta Morigi

Publication date: 11 January 2012

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2011.02.041

zbMATH Keywords

finite groupsprime divisors3-generator subgroupssubgroup indices

Mathematics Subject Classification ID

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

Generating minimally transitive permutation groups. ⋮ On boundedly generated subgroups of profinite groups. ⋮ The minimum generating set problem

Cites Work

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• On the probability of generating finite groups with a unique minimal normal subgroup.
• Some applications of the first cohomology group
• Generators for finite groups with a unique minimal normal subgroup
• Probabilistic generation of finite simple groups
• Generation of almost simple groups
• On elements of prime-power index in finite groups.
• The X-Dirichlet polynomial of a finite group
• On the number of generators and composition length of finite linear groups

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