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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.
