Derived length and character degrees of solvable groups

Moretó, Alexander

doi:10.1090/S0002-9939-03-07251-4

Derived length and character degrees of solvable groups
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Proc. Amer. Math. Soc. 132 (2004), 1599-1604 Request permission

Abstract:

We prove that the derived length of a solvable group is bounded in terms of certain invariants associated to the set of character degrees and improve some of the known bounds. We also bound the derived length of a Sylow $p$-subgroup of a solvable group by the number of different $p$-parts of the character degrees of the whole group.

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