New refinements of the McKay conjecture for arbitrary finite groups

2004/11/08 by I. M. Isaacs, G. Navarro · 1 citation
Mathematics · #math.GR #msc:20C15

paper · pdf

published as Ann. of Math. (2), Vol. 156 (2002), no. 1, 333--344 · 12 pages published version

arxiv created 2004/11/08 · arxiv updated 2009/12/01

Abstract

Let G be an arbitrary finite group and fix a prime number p. The McKay conjecture asserts that G and the normalizer in G of a Sylow p-subgroup have equal numbers of irreducible characters with degrees not divisible by p. The Alperin-McKay conjecture is a version of this as applied to individual Brauer p-blocks of G. We offer evidence that perhaps much stronger forms of both of these conjectures are true.

Cited by

• The Isaacs--Navarro Galois conjecture

Related

• Degree divisibility in Alperin-McKay correspondences
• The McKay Conjecture on character degrees
• The McKay conjecture with group automorphisms and the Okuyama-Wajima argument
• The inductive McKay-Navarro conditions for the prime 2 and some groups of Lie type
• Alperin's bound and normal Sylow subgroups