Character degree graphs and normal subgroups

DOI10.1090/S0002-9947-03-03462-7zbMath1034.20009OpenAlexW1560354019MaRDI QIDQ4441749

I. M. Isaacs

Publication date: 7 January 2004

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-03-03462-7

zbMATH Keywords

finite solvable groupsconnected componentsnormal subgroupsirreducible characterscharacter degreesnilpotent lengthscommon-divisor 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 (11)

An answer to a question of Isaacs on character degree graphs. ⋮ Common Divisor Character Degree Graphs of Solvable Groups with Four Vertices ⋮ Taketa's theorem for relative character degrees. ⋮ Graphs of nonsolvable groups with four degree-vertices. ⋮ Recognition of \(\text{PSL}(2,p)\) by order and some information on its character degrees where \(p\) is a prime ⋮ Disconnectedness and Diameters of Degree Graphs Associated with Normal Subgroups# ⋮ Recognition of the simple group \(\mathrm{PSL}(2,p^2)\) by character degree graph and order. ⋮ An overview of graphs associated with character degrees and conjugacy class sizes in finite groups. ⋮ A CHARACTERIZATION OF PSL(4,p) BY SOME CHARACTER DEGREE ⋮ Some Extensions of PSL(2,p²) are Uniquely Determined by Their Complex Group Algebras ⋮ A new characterization for the simple group PSL(2, p 2) by order and some character degrees

Cites Work

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• Irreducible character degrees and normal subgroups
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• Degree problems II π - separable character degrees
• A note on character degrees of finite solvable groups
• On the character degree graph of solvable groups. II. Discon- nected graphs
• Endliche Gruppen I
• Bounding Fitting heights of character degree graphs

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