The non-isolated vertices in the generating graph of a direct powers of simple groups.

DOI10.1007/s10801-012-0365-1zbMath1276.20026OpenAlexW1964770012MaRDI QIDQ1935380

Andrea Lucchini, Eleonora Crestani

Publication date: 15 February 2013

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10801-012-0365-1

zbMATH Keywords

finite groups2-generator groupsdiameters of graphsdirect powers of simple groupsgenerating graphs

Mathematics Subject Classification ID

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) Finite simple groups and their classification (20D05)

Related Items

Maximal cocliques in the generating graphs of the alternating and symmetric groups ⋮ On the connectivity of the non-generating graph ⋮ On the generating graph of direct powers of a simple group. ⋮ The generating graph of finite soluble groups. ⋮ The diameter of the generating graph of a finite soluble group ⋮ Maximal subgroups of finite groups avoiding the elements of a generating set ⋮ The non-commuting, non-generating graph of a non-simple group ⋮ The generating graph of a profinite group ⋮ The non-commuting, non-generating graph of a nilpotent group ⋮ CONNECTED COMPONENTS IN THE INVARIABLY GENERATING GRAPH OF A FINITE GROUP ⋮ The virtually generating graph of a profinite group

Cites Work

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• Sets of elements that pairwise generate a linear group
• On the clique number of the generating graph of a finite group

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