Enumerating finite groups and their defining relations

DOI10.1515/jgth.1998.002zbMath0892.20018OpenAlexW2082132520MaRDI QIDQ4375859

Avinoam Mann

Publication date: 4 June 1998

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jgth.1998.002

zbMATH Keywords

relationspresentationsfinite \(p\)-groupsgeneratorsasymptotic enumerationnumbers of finite groupssolvable groups

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Generators, relations, and presentations of groups (20F05) Asymptotic results on counting functions for algebraic and topological structures (11N45) Finite nilpotent groups, (p)-groups (20D15)

Related Items

Enumerating finite groups and their defining relations. II., Describing finite groups by short first-order sentences, Presentations of finite simple groups: A quantitative approach, Enumerating boundedly generated finite groups., Pro-finite presentations, Short presentations for three-dimensional unitary groups., Large normal subgroup growth and large characteristic subgroup growth, Finite groups and hyperbolic manifolds

Cites Work

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• Enumerating finite groups of given order
• ENUMERATING FINITE GROUPS
• Enumerating p -Groups. I: Inequalities
• Composition Factors from the Group Ring and Artin's Theorem on Orders of Simple Groups
• Enumerating p -Groups
• AN ENUMERATION THEOREM FOR FINITE GROUPS