Modularly irreducible characters and normal subgroups

Abstract

Let $G$ be a finite $p$-solvable group, where $p$ is an odd prime. Suppose that $\chi \in \operatorname{Irr}(G)$ lifts an irreducible $p$-Brauer character. If $G/N$ is a $p$-group, then we prove that the irreducible constituents of $\chi_{N}$ lift irreducible Brauer characters of $N$. This result was proven for $|G|$ odd by J.P. Cossey.