Zeros of Monomial Brauer Characters

Let $G$ be a finite group and $p$ be a fixed prime. A $p$-Brauercharacter of $G$ is said to be monomial if it is induced from alinear $p$-Brauer character of some subgroup (not necessarilyproper) of $G$. Denote by ${rm IBr}_{m}(G)$ the set of irreduciblemonomial $p$-Brauer characters of $G$. Let $H=G''{bf O}^{p''}(G)$ bethe smallest normal subgroup such that $G/H$ is an abelian$p''$-group. Suppose that $gin G$ is a $p$-regular element and theorder of $gH$ in the factor group $G/H$ does not divide $|{rmIBr}_{m}(G)|$. Then there exists $varphiin {rm IBr}_{m}(G)$ suchthat $varphi(g)=0$.