Products of characters and derived length

Let G be a finite solvable group and chi is an element of 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(chi) over bar We also discuss other properties of the decomposition of chi(chi) over bar into its irreducible constituents. (C) 2003 Elsevier Inc. All rights reserved.