Products of characters and derived length

Abstract

Let G be a finite solvable group and $χ\in \Irr(G)$ be a faithful character. We show that the derived length of G is bounded by a linear function of the number of distinct irreducible constituents of $\chi \bar{\chi }$. We also discuss other properties of the decomposition of $\chi \bar{\chi }$ into its irreducible constituents.

12 pages, to appear J. Algebra