McKay conjecture

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This article is about a conjecture in the following area in/related to group theory: representation theory. View all conjectures and open problems

Statement

Let G be a finite group and p a prime number dividing the order of G. Let P be a p-Sylow subgroup of G. Then the number of irreducible complex characters of G whose order is not divisible by p, equals the number of irreducible complex characters of N_G(P), whose order is not divisible by p.

In other words, if Irr_{p'}(G) denotes the number of irreducible characters of G whose order is not divisible by p:

Irr_{p'}(G) = Irr_{p'}N_G(P)