The relative McKay conjecture

Let $G$ be a finite group, let $L\unlhd G$, let $P/L\in\operatorname{Syl}_p(G/L)$, and let $\nu\in\operatorname{Irr}(L)$ be $P$-invariant. Write $\operatorname{Irr}_{p'}(G\mid\nu)$ for the irreducible characters of $G$ lying above $\nu$ whose degrees are prime to $p$. Relative McKay conjecture. One has

$$|\operatorname{Irr}_{p'}(G\mid\nu)|=|\operatorname{Irr}_{p'}(N_G(P)\mid\nu)|.$$

This generalizes McKay's counting assertion to a normal subgroup and a prescribed invariant character. The source presents it as a key generalization used in reduction arguments; no general proof is stated.