Inducing $\pi$-partial characters with a given vertex

Abstract

Let $G$ be a solvable group. Let $p$ be a prime and let $Q$ be a $p$-subgroup of a subgroup $V$. Suppose $ϕ\in \ibr G$. If either $|G|$ is odd or $p=2$, we prove that the number of Brauer characters of $H$ inducing $\varphi$ with vertex $Q$ is at most $|\norm GQ: \norm VQ|$.