Abstract
Let G be a solvable group with five character degrees. Suppose that there is some prime p so that G/O p(G) is not Abelian. Also, assume that cd(G) contains a degree that is not divisible by p. Under these hypotheses, we show that the derived length of G is at most 4.
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Lewis, M.L. Derived Lengths of Solvable Groups Having Five Irreducible Character Degrees II. Algebras and Representation Theory 5, 277–304 (2002). https://doi.org/10.1023/A:1016535504003
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DOI: https://doi.org/10.1023/A:1016535504003