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A NOTE ON DERIVED LENGTH AND CHARACTER DEGREES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 103 / Issue 2 / April 2021
- Published online by Cambridge University Press:
- 13 July 2020, pp. 271-277
- Print publication:
- April 2021
-
- Article
- Export citation
-
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.
