Groups whose prime graph on conjugacy class sizes has few complete vertices.

DOI10.1016/j.jalgebra.2012.04.013zbMath1268.20033OpenAlexW2073155060MaRDI QIDQ1936124

Emanuele Pacifici, Carlo Casolo, Silvio Dolfi, Lucia Sanus

Publication date: 21 February 2013

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2012.04.013

zbMATH Keywords

finite groupsregular graphsconjugacy class sizesprime graphscomplete vertices

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) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (2)

Finite groups whose prime graph on class sizes is a block square ⋮ Groups whose prime graph on class sizes has a cut vertex

Cites Work

• Character degree graphs with no complete vertices.
• Character degrees, class sizes, and normal subgroups of a certain class of \(p\)-groups
• Finite groups with small conjugacy classes
• Fitting heights and the character degree graph
• Arithmetical conditions on the length of the conjugacy classes of a finite group
• On independent sets in the class graph of a finite group.
• Products of primes in conjugacy class sizes and irreducible character degrees.
• Fitting Height and Diameter of Character Degree Graphs
• Some linear actions of finite groups with q′-orbits
• On a Graph Related to Conjugacy Classes of Groups
• Orbit sizes, local subgroups and chains of p-groups
• The Diameter of a Conjugacy Class Graph of Finite Groups

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