Products of characters and derived length II

Abstract

Let $G$ be a finite solvable group and $χ, ψ\in \Irr(G)$ be complex characters of $G$. Let $\alpha$ be an irreducible constituent of the product $\chi \psi$. We show that the derived length of $\Ker(α)/\Ker(χψ)$ is bounded by a linear function on the number of distinct irreducible constituents of $\chi \psi$

To appear Journal of Group Theory