Zeros of Monomial Brauer Characters

Abstract

Let G be a finite group and p be a fixed prime. A p-Brauer character of G is said to be monomial if it is induced from a linear p-Brauer character of some subgroup (not necessarily proper) of G. Denote by IBr _m(G) the set of irreducible monomial p-Brauer characters of G. Let H = G′O ^p′ (G) be the smallest normal subgroup such that G/H is an abelian p′-group. Suppose that g ∈ G is a p-regular element and the order of gH in the factor group G/H does not divide |IBr _m(G)|. Then there exists φ ∈ IBr _m(G) such that φ(g) = 0.

Keywords

Brauer character / Finite group / Vanishing regular element / Monomial Brauer character

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