Commuting Involution Graphs in Special Linear Groups

DOI10.1081/AGB-200034023zbMath1074.20033MaRDI QIDQ3158378

Sarah B. Perkins, C. Bates, David M. Bundy, Peter J. Rowley

Publication date: 25 January 2005

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

zbMATH Keywords

diametersspecial linear groupscommuting involution graphs

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Linear algebraic groups over arbitrary fields (20G15) 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)

Related Items (14)

Structures and topological indices of commuting involution graphs ⋮ On \(\pi\)-product involution graphs in symmetric groups ⋮ On coprimality graphs for symmetric groups. ⋮ On commuting involution graphs for the small Ree groups ⋮ INVOLUTION GRAPHS WHERE THE PRODUCT OF TWO ADJACENT VERTICES HAS ORDER THREE ⋮ Finite groups, 2-generation and the uniform domination number ⋮ Commuting involution graphs in classical affine Weyl groups ⋮ The diameter of the commuting graph of a finite group with trivial centre. ⋮ Commuting involution graphs for 4-dimensional projective symplectic groups ⋮ Commuting involution graphs for sporadic simple groups. ⋮ On commuting graphs for elements of order 3 in symmetric groups ⋮ Conjugate $p$-elements of full support that generate the wreath product $C_{p}wr C_{p}$ ⋮ Commuting involution graphs for certain exceptional groups of Lie type ⋮ Description of the first disc Δ1(t) of the commuting graph C(G, X) for elements of order three in symmetric groups

Cites Work

• Anisotropic groups of type \(A_n\) and the commuting graph of finite simple groups.
• On groups of even order
• Commuting involution graphs for symmetric groups.
• Finite groups generated by 3-transpositions. I
• Commuting involution graphs for finite Coxeter groups
• Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable
• The commuting graph of minimal nonsolvable groups

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