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The set of character degrees of a finite group does not determine its solvability


Author: Gabriel Navarro
Journal: Proc. Amer. Math. Soc. 143 (2015), 989-990
MSC (2010): Primary 20C15
DOI: https://doi.org/10.1090/S0002-9939-2014-12321-5
Published electronically: November 4, 2014
MathSciNet review: 3293716
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Abstract | References | Similar Articles | Additional Information

Abstract: We find a pair of groups, one solvable and the other non-solvable, with the same set of character degrees.


References [Enhancements On Off] (What's this?)

  • [1] Richard Brauer, Representations of finite groups, Lectures on Modern Mathematics, Vol. I, Wiley, New York, 1963, pp. 133-175. MR 0178056 (31 #2314)
  • [2] Bertram Huppert, Some simple groups which are determined by the set of their character degrees. I, Illinois J. Math. 44 (2000), no. 4, 828-842. MR 1804317 (2001k:20009)
  • [3] Gabriel Navarro, Problems in character theory, Character theory of finite groups, Contemp. Math., vol. 524, Amer. Math. Soc., Providence, RI, 2010, pp. 97-125. MR 2731923 (2012a:20014), https://doi.org/10.1090/conm/524/10350

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Additional Information

Gabriel Navarro
Affiliation: Departament d’Àlgebra, Universitat de València, 46100 Burjassot, València, Spain
Email: gabriel@uv.es

DOI: https://doi.org/10.1090/S0002-9939-2014-12321-5
Keywords: Character degrees, solvability, finite groups
Received by editor(s): July 3, 2013
Published electronically: November 4, 2014
Additional Notes: The authors research was partially supported by the Spanish Ministerio de Educación y Ciencia, proyecto MTM2010-15296, and Prometeo/Generalitat Valenciana
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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