Malle–Navarro–Tiep conjecture on Brauer characters and normal Sylow subgroups

Let $G$ be a finite group, let $p$ be a prime, and let $P$ be a Sylow $p$-subgroup of $G$. Write $\operatorname{IBr}(G)$ for the set of $p$-Brauer characters of $G$. Malle–Navarro–Tiep conjecture. The subgroup $P$ is normal in $G$ if and only if

$$|\operatorname{IBr}(G)|=|\operatorname{IBr}(\operatorname{N}_G(P))|.$$

This conjecture characterises normality of a Sylow subgroup through the number of Brauer characters. The paper reduces it to a question about finite simple groups and proves it for $p=2$, while the general statement remains open.