On a Commuting Graph on Conjugacy Classes of Groups

DOI10.1080/00927870802502779zbMath1187.20027OpenAlexW2103492091MaRDI QIDQ3646322

Patrizia Longobardi, Marcel Herzog, Mercede Maj

Publication date: 20 November 2009

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

Full work available at URL: https://doi.org/10.1080/00927870802502779

zbMATH Keywords

conjugacy classesperiodic groupslocally finite groupsconjugacy class graphsnon-commuting graphs

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Solvable groups, supersolvable groups (20F16) Periodic groups; locally finite groups (20F50) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (20)

Finite groups whose commuting conjugacy class graphs have isolated vertices ⋮ Commuting Conjugacy Class Graph of Finite CA-Groups ⋮ Counting Centralizers of a Finite Group with an Application in Constructing the Commuting Conjugacy Class Graph ⋮ Commuting graph of \(A \)-orbits ⋮ Super graphs on groups. I ⋮ Automorphism group of the commuting graph of \(2\times 2\) matrix ring over \(\mathbb{Z}_{p^s}\) ⋮ Triangle-free commuting conjugacy class graphs. ⋮ Unnamed Item ⋮ On the class of KN-complete groups ⋮ Commuting graph of a group action with few edges ⋮ Solvable conjugacy class graph of groups ⋮ The commuting conjugacy class graphs of finite groups with a given property ⋮ Unnamed Item ⋮ The power graph on the conjugacy classes of a finite group ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On a graph related to permutability in finite groups ⋮ On the nilpotent conjugacy class graph of groups ⋮ On Certain Weak Engel-Type Conditions in Groups ⋮ N-critical graph of finite groups

Cites Work

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• On the Diameter of a Graph Related to Conjugacy Classes of Groups
• Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable
• Groups Whose Elements Have Bounded Orders
• Embedding Theorems for Groups
• The commuting graph of minimal nonsolvable groups

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