On the Clique Numbers of Non-commuting Graphs of Certain Groups

DOI10.1142/S1005386710000581zbMath1227.20021arXiv0903.0692MaRDI QIDQ3162650

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Publication date: 20 October 2010

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

Full work available at URL: https://arxiv.org/abs/0903.0692

zbMATH Keywords

finite groupsSuzuki groupsspecial linear groupsminimal simple groupsnon-commuting graphsnon-solvable groupspairwise non-commuting elements of groupsclique numbers of graphs

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) 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) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (7)

Abelian covers of alternating groups ⋮ Abelian covers and non-commuting sets in a non-abelian \(p\)-group which its central quotient is metacyclic ⋮ The Probability That an Ordered Pair of Elements is an Engel Pair ⋮ Non-permutability graph of subgroups ⋮ ON NONCOMMUTING SETS AND CENTRALISERS IN INFINITE GROUPS ⋮ A generalization of Neumann's question ⋮ Finite groups determined by the number of element centralizers

Uses Software

• GAP

Cites Work

• Minimal covers of \(S_ n\) by abelian subgroups and maximal subsets of pairwise noncommuting elements. II
• Minimal covers of \(S_ n\) by Abelian subgroups and maximal subsets of pairwise noncommuting elements
• Some applications of graph theory to finite groups
• Non-commuting graph of a group.
• Sur la dimension cohomologique des groupes profinis
• FINITE AXIOMATIZATION OF FINITE SOLUBLE GROUPS
• Semisimple groups with the rewriting property Q₅
• Nonsolvable finite groups all of whose local subgroups are solvable
• Endliche Gruppen I

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