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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Derived length and character degrees of solvable groups


Author: Alexander Moretó
Journal: Proc. Amer. Math. Soc. 132 (2004), 1599-1604
MSC (2000): Primary 20C15, 20D15
Published electronically: November 14, 2003
MathSciNet review: 2051119
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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 $p$-subgroup of a solvable group by the number of different $p$-parts of the character degrees of the whole group.


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Additional Information

Alexander Moretó
Affiliation: Departament d’Àlgebra, Universitat de València, 46100 Burjassot. València, Spain
Email: mtbmoqua@lg.ehu.es

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07251-4
PII: S 0002-9939(03)07251-4
Received by editor(s): December 5, 2002
Received by editor(s) in revised form: February 13, 2003
Published electronically: November 14, 2003
Additional Notes: This research was supported by the Basque Government, the Spanish Ministerio de Ciencia y Tecnología, grant BFM2001-0180, and the FEDER
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2003 American Mathematical Society