A Note On Derived Length and Character Degrees

Abstract

Isaacs and Seitz conjectured that the derived length of a finite solvable group G is bounded by the cardinality of the set of all irreducible character degrees of G. We prove that the conjecture holds for G if the degrees of nonlinear monolithic characters of G having the same kernels are distinct. Also, we show that the conjecture is true when G has at most three nonlinear monolithic characters. We give some sufficient conditions for the inequality related to monolithic characters or real-valued irreducible characters of G when the commutator subgroup of G is supersolvable.