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Brauer characters and rationality

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Abstract

A finite group \(G\) has no non-trivial rational-valued irreducible \(p\)-Brauer characters if and only if \(G\) has no non-trivial rational elements of order not divisible by \(p\).

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References

  1. Burkhardt, R.: Die Zerlegungsmatrizen der Gruppen PSL\((2, p^{f})\). J. Algebra 40, 75–96 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  2. Digne, F., Michel, J.: Representations of Finite Groups of Lie Type, London Mathematical Society Student Texts 21. Cambridge University Press, Cambridge (1991)

    Book  Google Scholar 

  3. Gross, B.H.: Group representations and lattices. J. Am. Math. Soc. 3, 929–960 (1990)

    Article  MATH  Google Scholar 

  4. Isaacs, I.M.: Character Theory of Finite Groups. Dover, New York (1994)

    MATH  Google Scholar 

  5. Navarro, G.: Characters and Blocks of Finite Groups. Cambridge University Press, Cambridge (1998)

    Book  MATH  Google Scholar 

  6. Navarro, G., Tiep, P.H.: Rational Brauer characters. Math. Annalen 335, 675–686 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Navarro, G., Tiep, P.H.: Rational irreducible characters and rational conjugacy classes in finite groups. Am. Math. Soc. 360, 2443–2465 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Navarro, G., Tiep, P.H., Turull, A.: Brauer characters with cyclotomic field of values. J. Pure Appl. Algebra 212, 628–635 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. Tiep, P.H., Zalesskii, A.E.: Some characterizations of the Weil representations of symplectic and unitary groups. J. Algebra 192, 130–165 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  10. Wolf, T.R.: Character correspondences in solvable groups. Ill. J. Math. 22, 327–340 (1978)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Departament d’Àlgebra, Universitat de València, 46100 , Burjassot, Valencia, Spain

    Gabriel Navarro

  2. Department of Mathematics, University of Arizona, Tucson, AZ, 85721, USA

    Pham Huu Tiep

Authors
  1. Gabriel Navarro
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  2. Pham Huu Tiep
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Corresponding author

Correspondence to Pham Huu Tiep.

Additional information

The research of the first author is supported by the Prometeo/Generalitat Valenciana, Proyectos MTM2010-15296. The second author gratefully acknowledges the support of the NSF (grants DMS-0901241 and DMS-1201374).

The authors are grateful to the referee for careful reading and helpful comments on the paper.

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Navarro, G., Tiep, P.H. Brauer characters and rationality. Math. Z. 276, 1101–1112 (2014). https://doi.org/10.1007/s00209-013-1234-x

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  • DOI: https://doi.org/10.1007/s00209-013-1234-x

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