Finite groups with a given set of character degrees.

DOI10.1007/S10468-015-9576-1zbMATH Open1348.20007OpenAlexW2246900470MaRDI QIDQ287498

Mark L. Lewis, Farideh Shafiei, A. Iranmanesh, Kamal Aziziheris

Publication date: 20 May 2016

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10468-015-9576-1

zbMATH Keywords

finite solvable groupsirreducible complex characterscharacter degreesderived lengthsTaketa inequalitycharacter degree sets

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)

Cites Work

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• Bounding the derived length for a given set of character degrees.
• Extending the Steinberg representation
• Determining group structure from sets of irreducible character degrees
• Irreducible character degrees and normal subgroups
• Groups having three complex irreducible character degrees
• Some character degree conditions implying solvability of finite groups.
• Nonsolvable groups with few character degrees.
• Solvable groups whose degree graphs have two connected components
• Character degrees of extensions of PSL2(q) and SL2(q)
• Character degree graphs that are complete graphs
• Orbits and Stabilizers for Solvable Linear Groups
• Coprime Group Actions Fixing All Nonlinear Irreducible Characters
• Derived lengths of solvable groups satisfying the one-prime hypothesis
• Coprimeness among irreducible character degrees of finite solvable groups
• Degrees of Irreducible Characters and Normal p-Complements
• Half-Transitive Automorphism Groups
• Endliche Gruppen I
• Nonsolvable groups with no prime dividing three character degrees.
• Fitting heights of solvable groups with few character degrees
• Derived lengths of solvable groups having five irreducible character degrees. I.

Related Items (7)

The character degree ratio and composition factors of a finite group. ⋮ The exterior degree of a pair of finite groups. ⋮ The character co-degree sets and solvability ⋮ An overview on the bipartite divisor graph for the set of irreducible character degrees ⋮ Finite Groups Whose Irreducible Character Degrees Constitute Two Chains ⋮ Finite Groups Whose Character Degree Graphs Are Empty Graphs ⋮ Some simple groups which are determined by the set of their character degrees. I

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