Characters of prime degree

Abstract

Let $G$ be a finite nilpotent group, $\chi$ and $\psi$ be irreducible complex characters of $G$ of prime degree. Assume that $\chi (1)=p$. Then either the product $\chi \psi$ is a multiple of an irreducible character or $\chi \psi$ is the linear combination of at least $\frac{p+1}{2}$ distinct irreducible characters.

8 pages