The diameter of the generating graph of a finite soluble group

DOI10.1016/j.jalgebra.2017.08.020zbMath1426.20009arXiv1701.03346OpenAlexW2589708980MaRDI QIDQ2411394

Andrea Lucchini

Publication date: 20 October 2017

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

Full work available at URL: https://arxiv.org/abs/1701.03346

zbMATH Keywords

soluble groupsgenerating graph

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) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Distance in graphs (05C12)

Related Items (11)

On the connectivity of the non-generating graph ⋮ Some results on the join graph of finite groups ⋮ The non-commuting, non-generating graph of a non-simple group ⋮ Generating graphs of finite dihedral groups ⋮ The generating graph of a profinite group ⋮ The independence graph of a finite group ⋮ The non-commuting, non-generating graph of a nilpotent group ⋮ Connectivity of generating graphs of nilpotent groups ⋮ THE GENERATING GRAPH OF INFINITE ABELIAN GROUPS ⋮ Forbidden subgraphs in generating graphs of finite groups ⋮ The virtually generating graph of a profinite group

Cites Work

• The generating graph of finite soluble groups.
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• Probabilistic generation of finite simple groups. II.
• Pre-Frattini groups.
• Crowns and factorization of the probabilistic zeta function of a finite group.
• Probabilistic generation of finite simple groups
• The non-isolated vertices in the generating graph of a direct powers of simple groups.
• \(d\)-wise generation of prosolvable groups.
• On the clique number of the generating graph of a finite group
• Zu einem von B. H. und H. Neumann gestellten Problem
• The X-Dirichlet polynomial of a finite group
• Characterizations of schunck classes of finite groups
• Every Linear Transformation is a Sum of Nonsingular Ones

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