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2003•Proceedings of the American Mathematical SocietyOpen access

Derived length and character degrees of solvable groups

Alexander Moretó

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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 p -subgroup of a solvable group by the number of different p p -parts of the character degrees of the whole group.

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What this paper is about

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 p -subgroup of a solvable group by the number of different p p -parts of the character degrees of the whole group.

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Available 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 p -subgroup of a solvable group by the number of different p p -parts of the character degrees of the whole group.

Key concepts: Sylow theorems, Solvable group, Character (mathematics), Mathematics, Combinatorics, Bounded function, Group (periodic table), Set (abstract data type)

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