Products of characters and finite p-groups II

Abstract

Let p be a prime number. Let G be a finite p-group and $χ\in Irr(G)$. Denote by $\barχ \in Irr(G)$ the complex conjugate of $χ$. Assume that $χ(1)=p^n$. We show that the number of distinct irreducible constituents of the product $χ\barχ$ is at least $2n(p-1)+1$.