Brauer characters with cyclotomic field of values |
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Authors: | Gabriel Navarro Pham Huu Tiep |
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Institution: | a Facultat de Matemàtiques, Universitat de València, Burjassot, València 46100, Spain b Department of Mathematics, University of Florida, Gainesville, FL 32611, USA |
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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(2πi/q)). |
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Keywords: | 20C20 |
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