Products of characters and derived length

Edith Adan-Bante

Published 2003-04-25Version 1

Let G be a finite solvable group and $\chi\in \Irr(G)$ 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.