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′O^P′（G）; if g ∈ G^0 - H^0 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 9. The authors also show in this note that the sums of certain irreducible p-Brauer characters take the value zero on every element of G^0 - H^0.