McKay conjecture

In mathematics, specifically in the field of group theory, the McKay conjecture is a theorem of equality between two numbers: the number of irreducible complex characters of degree not divisible by a prime number ${\displaystyle p}$ for a given finite group and the same number for the normalizer in that group of a Sylow ${\displaystyle p}$-subgroup.

It is named after the Canadian mathematician John McKay, who originally stated a limited version of it as a conjecture in 1971, for the special case of ${\displaystyle p=2}$ and simple groups. The conjecture was later generalized by other mathematicians to a more general conjecture for any prime value of ${\displaystyle p}$ and more general groups.

In 2023, a proof of the general conjecture was announced by Britta Späth and Marc Cabanes.