Zeros of Primitive Characters

Abstract

. Let G be a finite group. An irreducible character χ of G is said to be primitive if χ 6 = ϑ G for any character ϑ of a proper subgroup of G . In this paper, we consider about the zeros of primitive characters. Denote by Irr pri ( G ) the set of all irreducible primitive characters of G . We proved that if g ∈ G and the order of gG ′ in the factor group G / G ′ does not divide | Irr pri ( G ) | , then there exists ϕ ∈ Irr pri ( G ) such that ϕ ( g )= 0.