New refinements of the McKay conjecture for arbitrary finite groups

By I. Isaacs, Gabriel Navarro. 2002

81 citations recorded by the source corpus.

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 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.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/025aee759c11540e41efb3bb3ae13a693773605e

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In Artificial Intelligence

In Discrete Mathematics and Combinatorics

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Citations in the corpus

A reduction theorem for the Alperin–McKay conjecture (2012, methodology): “IrrðbÞ such that yð1Þ ~PðyÞð1Þ ¼ m n for every y A IrrðBÞ: Hence the heights are preserved and ~P induces a bijection between Irr0ðBÞ and Irr0ðbÞ. r The bijection P from Proposition 6.6 satisfies also the congruence, conjectured by Isaacs–Navarro.”
A reduction theorem for the McKay conjecture (2007, background): “) More recently, Isaacs and Navarro [11] proposed a refinement of the McKay conjecture that subdivides each of the sets Irrp′(G) and Irrp′(N) into (p−1)/2 subsets depending on the degrees of the characters modulo p.”
The inductive Alperin–McKay and Blockwise Alperin Weight conditions for blocks with cyclic defect groups and odd primes (2013, unknown): “(This forms an inductive condition for the Isaacs–Navarro conjecture from [21].”