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New refinements of the McKay conjecture for arbitrary finite groups

I. M. Isaacs·G. Navarro
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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.

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I. M. Isaacs, G. Navarro. 2004-11-08. New refinements of the McKay conjecture for arbitrary finite groups. https://arxiv.org/abs/math/0411171

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