### 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) |
---|---|

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 2008 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Pure and Applied Algebra*,

*212*(3), 628-635. https://doi.org/10.1016/j.jpaa.2007.06.019

**Brauer characters with cyclotomic field of values.** / Navarro, Gabriel; Tiep, Pham Huu; Turull, Alexandre.

Research output: Contribution to journal › Article

*Journal of Pure and Applied Algebra*, vol. 212, no. 3, pp. 628-635. https://doi.org/10.1016/j.jpaa.2007.06.019

}

TY - JOUR

T1 - Brauer characters with cyclotomic field of values

AU - Navarro, Gabriel

AU - Tiep, Pham Huu

AU - Turull, Alexandre

PY - 2008/3

Y1 - 2008/3

N2 - 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)).

AB - 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)).

UR - http://www.scopus.com/inward/record.url?scp=35848935226&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35848935226&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2007.06.019

DO - 10.1016/j.jpaa.2007.06.019

M3 - Article

AN - SCOPUS:35848935226

VL - 212

SP - 628

EP - 635

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 3

ER -