Derived length when a product of characters has two nonprincipal irreducible constituents

摘要

We study the situation where a solvable group G has a faithful irreducible character. such that chi(chi) over bar has exactly two distinct nonprincipal irreducible constituents. We prove that G has derived length bounded above by 8, and provide an example of such a group having derived length 8. In particular, this improves upon a result of Adan-Bante.