Products of characters and finite p-groups II

Abstract.

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