### Abstract

It has been shown in an earlier paper [G. Navarro, Pham Huu Tiep, Rational Brauer characters, Math. Ann. 335 (2006) 675-686] that, for any odd prime p, every finite group of even order has a non-trivial rational-valued irreducible p-Brauer character. For p = 2 this statement is no longer true. In this paper we determine the possible non-abelian composition factors of finite groups without non-trivial rational-valued irreducible 2-Brauer characters. We also prove that, if p ≠ q are primes, then any finite group of order divisible by q has a non-trivial irreducible p-Brauer character with values in the cyclotomic field Q (exp (2 π i / q)).

Original language | English (US) |
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Pages (from-to) | 628-635 |

Number of pages | 8 |

Journal | Journal of Pure and Applied Algebra |

Volume | 212 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2008 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Navarro, G., Tiep, P. H., & Turull, A. (2008). Brauer characters with cyclotomic field of values.

*Journal of Pure and Applied Algebra*,*212*(3), 628-635. https://doi.org/10.1016/j.jpaa.2007.06.019