McKay conjecture

In mathematics, specifically in the field of group theory, the McKay Conjecture is a conjecture of equality between the number of irreducible complex characters of degree not divisible by a prime number formula_1 to that of the normalizer of a Sylow formula_1-subgroup. It is named after Canadian mathematician John McKay.
Statement.
Suppose formula_1 is a prime number, formula_4 is a finite group, and formula_5 is a Sylow formula_1-subgroup. Define
where formula_8 denotes the set of complex irreducible characters of the group formula_4. The McKay conjecture claims the equality
where formula_11 is the normalizer of formula_12 in formula_4.