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

Let $G$ be a solvable group. Let $p$ be a prime and let $Q$ be a $p$-subgroup of a subgroup $V$. Suppose $\varphi \in \text{ibr}G$. If either $\mathrm{\mid }G\mathrm{\mid }$ is odd or $p = 2$,weprovethatthenumberofBrauercharactersof$H$inducing$\phi$ with vertex $Q$ is at most $\mathrm{\mid }\text{norm}GQ:\text{norm}VQ\mathrm{\mid }$.