Square character degree graphs yield direct products.

DOI10.1016/j.jalgebra.2011.09.016zbMath1251.20011arXiv1105.2799OpenAlexW1969944202MaRDI QIDQ420680

Qingyun Meng, Mark L. Lewis

Publication date: 23 May 2012

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

Full work available at URL: https://arxiv.org/abs/1105.2799

zbMATH Keywords

finite solvable groupsirreducible complex charactersdirect productssquarescharacter degreescharacter degree graphs

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) 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 (10)

n-Exact character graphs ⋮ Regular character degree graphs. ⋮ Finite groups with K₅-free prime graphs ⋮ Prime graphs of finite groups with a small number of triangles. ⋮ $4$-Regular prime graphs of nonsolvable groups ⋮ Bipartite divisor graph for the set of irreducible character degrees ⋮ Solvable groups whose character degree graphs generalize squares ⋮ K₄-free character graphs with seven vertices ⋮ Unnamed Item ⋮ Finite groups with \(K_4\)-free prime graphs.

Cites Work

• Determining group structure from sets of irreducible character degrees
• Solvable groups whose degree graphs have two connected components
• On the character degree graph of solvable groups. II. Discon- nected graphs
• Bounding Fitting heights of character degree graphs
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