TY - JOUR

T1 - Brauer characters with cyclotomic field of values

AU - Navarro, Gabriel

AU - Tiep, Pham Huu

AU - Turull, Alexandre

N1 - Funding Information:
The first author is partially supported by the Ministerio de Educación y Ciencia proyecto MTM2004-06067-C02-01. The second author gratefully acknowledges the support of the NSF (grant DMS-0600967) and the NSA (grant H98230-04-0066). The third author gratefully acknowledges the support of the NSA (grant MDA904-03-1-0013). Part of the paper was written while the second author was participating in the Special Semester on Group Representation Theory at the Bernoulli Center, Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland. It is a pleasure to thank the organizers, Profs. M. Geck, D. Testerman, and J. Thevenaz for the generous hospitality and support and stimulating environment. The authors are grateful to C. Bonnafé for writing up Proposition 2.1 and Corollaries 2.2–2.4 and kindly letting them to include this material in the paper. The authors also thank J. Müller for the helpful discussions.

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)).

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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 -