${\rm B}_π$-characters and quotients

Let $π$ be a set of primes, and let $G$ be a finite $π$-separable group. We consider the Isaacs ${\rm B}_π$-characters. We show that if $N$ is a normal subgroup of $G$, then ${\rm B}_π(G/N) = {\rm Irr} (G/N) \cap {\rm B}_π(G)$.

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