Generating sets of finite groups

DOI10.1090/tran/7248zbMath1429.20017arXiv1609.06077OpenAlexW3106356225MaRDI QIDQ4567904

Colva M. Roney-Dougal, Peter J. Cameron, Andrea Lucchini

Publication date: 20 June 2018

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

Full work available at URL: https://arxiv.org/abs/1609.06077

zbMATH Keywords

generationfinite groupgenerating graph

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Finite simple groups and their classification (20D05)

Related Items (7)

Maximal cocliques in the generating graphs of the alternating and symmetric groups ⋮ A note on maximal subgroups and conjugacy classes of finite groups ⋮ The independence graph of a finite group ⋮ GENERATING MAXIMAL SUBGROUPS OF FINITE ALMOST SIMPLE GROUPS ⋮ An algorithm for finding minimal generating sets of finite groups ⋮ Graphs defined on groups ⋮ On the semigroup rank of a group

Uses Software

• Magma
• OEIS

Cites Work

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• The largest size of a minimal generating set of a finite group.
• The generating graph of finite soluble groups.
• Invariable generation and the Chebotarev invariant of a finite group.
• Bias of group generators in the solvable case.
• \(1\tfrac 12\)-generation of finite simple groups
• Walks on generating sets of groups
• The Magma algebra system. I: The user language
• A theorem on random matrices and some applications
• Maximal independent generating sets of the symmetric group
• Covering the symmetric groups with proper subgroups.
• Probabilistic generation of finite simple groups
• Simple groups, probabilistic methods, and a conjecture of Kantor and Lubotzky
• Sets of elements that pairwise generate a linear group
• Generation and random generation: from simple groups to maximal subgroups.
• Simple groups admit Beauville structures
• On the clique number of the generating graph of a finite group
• Zu einem von B. H. und H. Neumann gestellten Problem
• Hamiltonian cycles in the generating graphs of finite groups
• CLASSIFYING COPOLAR SPACES AND GRAPHS
• On Random Generation of the Symmetric Group
• ON THE GENERATING GRAPH OF A SIMPLE GROUP
• The minimal generating sets of of size four
• Classes of Finite Groups

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