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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Rational irreducible characters and rational conjugacy classes in finite groups
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by Gabriel Navarro and Pham Huu Tiep PDF
Trans. Amer. Math. Soc. 360 (2008), 2443-2465 Request permission


We prove that a finite group $G$ has two rational-valued irreducible characters if and only if it has two rational conjugacy classes, and determine the structure of any such group. Along the way we also prove a conjecture of Gow stating that any finite group of even order has a non-trivial rational-valued irreducible character of odd degree.
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Additional Information
  • Gabriel Navarro
  • Affiliation: Facultat de Matemàtiques, Universitat de València, Burjassot, València 46100, Spain
  • MR Author ID: 129760
  • Email:
  • Pham Huu Tiep
  • Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
  • MR Author ID: 230310
  • Email:
  • Received by editor(s): February 6, 2006
  • Published electronically: November 27, 2007
  • Additional Notes: The first author was partially supported by the Ministerio de Educación y Ciencia proyecto MTM2004-06067-C02-01.
    Part of this work was done while the first author visited the University of Florida in Gainesville, and he would like to thank the Mathematics Department for its hospitality. Special thanks are due to A. Turull. This paper benefited from conversations with M. Isaacs, A. Moretó, A. Turull and B. Wilkens. The authors are grateful to the referee for pointing out some inaccuracies in an earlier version of the paper as well as for helpful comments that greatly improved the exposition of the paper.
    The second author gratefully acknowledges the support of the NSA and the NSF

  • Dedicated: Dedicated to Professor Michel Broué on the occasion of his sixtieth birthday
  • © Copyright 2007 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 2443-2465
  • MSC (2000): Primary 20C15, 20C33, 20E45
  • DOI:
  • MathSciNet review: 2373321