Strengthening the McKay conjecture to include local fields and local Schur indices.

DOI10.1016/j.jalgebra.2005.12.035zbMath1173.20008OpenAlexW2077918630WikidataQ122861236 ScholiaQ122861236MaRDI QIDQ934028

Alexandre Turull

Publication date: 29 July 2008

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2005.12.035

zbMATH Keywords

finite groupsClifford theorysporadic simple groupsBrauer groupsirreducible complex charactersMcKay conjecturecharacter correspondencesSchur indices

Mathematics Subject Classification ID

Modular representations and characters (20C20) Representations of sporadic groups (20C34)

Related Items (20)

On Clifford theory with Galois action ⋮ The Brauer-Clifford group. ⋮ Brauer-Clifford equivalence of full matrix algebras. ⋮ Galois-equivariant McKay bijections for primes dividing \(q - 1\) ⋮ Degree divisibility in character correspondences. ⋮ On the calculation of local invariants of irreducible characters ⋮ Height-zero characters and normal subgroups in \(p\)-solvable groups. ⋮ The strengthened Alperin weight conjecture for \(p\)-solvable groups. ⋮ The strengthened Broué abelian defect group conjecture for \(\mathrm{SL} (2,p^n)\) and \(\mathrm{GL} (2,p^n)\) ⋮ A reduction theorem for the Galois–McKay conjecture ⋮ A reduction theorem for the McKay conjecture. ⋮ Refinements of Dade's projective conjecture for \(p\)-solvable groups ⋮ Above the Glauberman correspondence. ⋮ Odd character correspondences in solvable groups. ⋮ The Navarro conjecture for the alternating groups ⋮ The fields of values of characters of degree not divisible byp ⋮ Correspondences Between 2-Brauer Characters of Solvable Groups ⋮ Characters, Brauer characters, and local Brauer groups ⋮ Character triple conjecture for \(p\)-solvable groups ⋮ Character correspondences in solvable groups.

Uses Software

• GAP

Cites Work

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• Schur indices and cyclic defect groups
• The McKay conjecture is true for the sporadic simple groups
• The McKay numbers of a subgroup of \(\text{GL}(n;q)\) containing \(\text{SL}(n;q)\)
• Schur indices and Schur groups
• The Schur indices of the irreducible characters of the special linear groups
• New refinements of the McKay conjecture for arbitrary finite groups
• Calculating Clifford classes for characters containing a linear character once.
• Clifford classes for some overgroups of the special linear groups.
• The Isaacs-Navarro conjecture for symmetric groups.
• Schur indices of characters of groups related to finite sporadic simple groups
• Schur indices and Schur groups. II.
• Character correspondences in solvable groups.

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