New refinements of the McKay conjecture for arbitrary finite groups

Details New refinements of the McKay conjecture for arbitrary finite groups New refinements of the McKay conjecture for arbitrary finite groups

2004-11-08

arxiv.org/abs/math/0411171v1

Ann. of Math. (2), Vol. 156 (2002), no. 1, 333--344

Mathematics

Group Theory

12 pages published version

Scientific paper

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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