The non-commuting, non-generating graph of a nilpotent group

DOI10.37236/9802zbMath1456.05072arXiv2008.09291OpenAlexW3081486720MaRDI QIDQ2223469

Colva M. Roney-Dougal, Peter J. Cameron, Saul D. Freedman

Publication date: 29 January 2021

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.09291

zbMATH Keywords

commuting graphgenerating graph

Mathematics Subject Classification ID

Nilpotent groups (20F18) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Finite simple groups and their classification (20D05)

Related Items (4)

Between the enhanced power graph and the commuting graph ⋮ The non-commuting, non-generating graph of a non-simple group ⋮ On groups with chordal power graph, including a classification in the case of finite simple groups ⋮ Graphs defined on groups

Uses Software

• Magma

Cites Work

• Andrews-Curtis and Nielsen equivalence relations on some infinite groups.
• Probabilistic generation of finite simple groups. II.
• On the Burnside problem for periodic groups
• On a 2-generated infinite 3-group: The presentation problem
• The Magma algebra system. I: The user language
• Maximal subgroups of direct products
• The non-isolated vertices in the generating graph of a direct powers of simple groups.
• Finite groups, 2-generation and the uniform domination number
• There is no upper bound for the diameter of the commuting graph of a finite group
• On the structure of the power graph and the enhanced power graph of a group
• The diameter of the generating graph of a finite soluble group
• The diameter of the commuting graph of a finite group with trivial centre.
• Non-commuting graph of a group.
• Das ``schiefe Produkt in der Gruppentheorie mit Anwendung auf die endlichen nichtkommutativen Gruppen mit lauter kommutativen echten Untergruppen und die Ordnungszahlen, zu denen nur kommutative Gruppen gehören
• The groups of order at most 2000
• MAXIMAL SUBGROUPS OF SOME NON LOCALLY FINITE p-GROUPS
• Nielsen equivalence in Gupta-Sidki groups

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