Zeros of Brauer characters

The authors obtain a sufficient condition to determine whether an element is a vanishing regular element of some Brauer character. More precisely, let G be a finite group and p be a fixed prime, and H = G′ Op′ (G); if g ∈ G0 - H0 with o(gH) coprime to the number of irreducible p-Brauer characters of G, then there always exists a nonlinear irreducible p-Brauer character which vanishes on g. The authors also showin this note that the sums of certain irreducible p-Brauer characters take the value zero on every element of G0 - H0.