Simple groups are characterized by their non-commuting graphs

DOI10.1515/jgt-2013-0021zbMath1293.20024OpenAlexW2047698945MaRDI QIDQ5402144

Andrew J. Woldar, Ronald M. Solomon

Publication date: 5 March 2014

Published in: jgth (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jgt-2013-0021

zbMATH Keywords

finite simple groups of Lie typeAAM conjecturenon-commuting graphs of groups

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (26)

Metric and strong metric dimension in commuting graphs of finite groups ⋮ Commuting graph of \(A \)-orbits ⋮ On characterization of a completely simple semigroup by its power graph and Green relations ⋮ Subgroup sum graphs of finite abelian groups ⋮ Eulerian properties of non-commuting and non-cyclic graphs of finite groups ⋮ On the lower bound for diameter of commuting graph of prime-square sized matrices ⋮ Non-commuting graphs and some bounds for commutativity degree of finite Moufang loops ⋮ On diameter of the commuting graph of a full matrix algebra over a finite field ⋮ Finite groups with isomorphic non-commuting graphs have the same nilpotency property ⋮ A conjecture related to the nilpotency of groups with isomorphic non-commuting graphs ⋮ The orthogonality relation classifies finite-dimensional formally real simple Jordan algebras ⋮ The diameter of the commuting graph of a finite group with trivial centre. ⋮ REALIZABILITY PROBLEM FOR COMMUTING GRAPHS ⋮ On the non-commuting graph in finite Moufang loops ⋮ Non-permutability graph of subgroups ⋮ The influence of the complete nonexterior square graph on some infinite groups ⋮ On diameter of components in commuting graphs ⋮ Graphs defined on groups ⋮ Non-commuting graphs of certain almost simple groups ⋮ Symmetrized Birkhoff-James orthogonality in arbitrary normed spaces ⋮ Some structural graph properties of the non-commuting graph of a class of finite Moufang loops ⋮ On groups covered by finitely many centralizers and domination number of the commuting graphs ⋮ Numerical bounds for the exterior degree of finite simple groups ⋮ Planar, Toroidal, and Projective Commuting and Noncommuting Graphs ⋮ EXTENDING RESULTS OF MORGAN AND PARKER ABOUT COMMUTING GRAPHS ⋮ Non-Commuting Graphs of Nilpotent Groups

This page was built for publication: Simple groups are characterized by their non-commuting graphs