Degrees of rational characters of finite groups.

DOI10.1016/j.aim.2009.12.023zbMath1200.20006OpenAlexW2074878864MaRDI QIDQ973938

Gabriel Navarro, Pham Hũ'u Tiêp

Publication date: 26 May 2010

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2009.12.023

zbMATH Keywords

character degreesGlauberman correspondencecomplex irreducible charactersclassification of finite simple groupsnormal \(p\)-complementsrational characters

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) Finite simple groups and their classification (20D05) Representations of finite groups of Lie type (20C33) Products of subgroups of abstract finite groups (20D40)

Related Items (22)

Odd-degree rational irreducible characters ⋮ Kernels of \(p'\)-degree irreducible characters ⋮ Real-imaginary conjugacy classes and real-imaginary irreducible characters in finite groups ⋮ Variations on the Itô-Michler theorem on character degrees ⋮ Brauer correspondent blocks with one simple module ⋮ A real version of Thompson's theorem on degrees ⋮ Methods and questions in character degrees of finite groups ⋮ Nonsolvable groups have a large proportion of vanishing elements ⋮ Finite groups with three rational conjugacy classes ⋮ Irreducible characters of even degree and normal Sylow 2-subgroups ⋮ 2-parts of real class sizes ⋮ Representation of finite groups: conjectures, reductions, and applications. ⋮ Characters of odd degree and Thompson's character degree theorem ⋮ Variations on average character degrees and \(p\)-nilpotence ⋮ The Ore conjecture. ⋮ Real class sizes and real character degrees ⋮ The average character degree and an improvement of the Itô-Michler theorem ⋮ Finite groups whose real-valued irreducible characters have prime power degrees ⋮ Real ordinary characters and real Brauer characters ⋮ McKay graphs for alternating and classical groups ⋮ On almost \(p\)-rational characters of \(p^{\prime}\)-degree ⋮ Unnamed Item

Uses Software

• GAP

Cites Work

• Unnamed Item
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• Characters of \(\pi\)-separable groups
• Real characters and degrees.
• Rationality and normal 2-complements.
• Representations of finite special linear groups in non-defining characteristic.
• Multiplicity-free permutation representations of finite linear groups
• Some generalizations of the Weil representations of the symplectic and unitary groups
• Tensor induction of generalized characters and permutation characters
• Real characters of \(p'\)-degree.
• Brauer characters with cyclotomic field of values.
• The McKay conjecture and Galois automorphisms.
• Cross-Characteristic Embeddings of Finite Groups of Lie Type
• Characters of Reductive Groups over a Finite Field. (AM-107)
• The Irreducible Representations of the Finite General Linear Groups
• Finite Covers, Cohomology and Homogeneous Structures
• Group Representations and Lattices
• Minimal characters of the finite classical groups
• Rational irreducible characters and rational conjugacy classes in finite groups
• Le Groupe GL_n Tordu, Sur un Corps Fini
• Characters of 𝑝’-degree with cyclotomic field of values

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