Rational Brauer characters

It is known that every finite group of even order has a non-trivial complex irreducible character which is rational valued. We prove the modular version of this result: If p is an odd prime and G is any finite group of even order, then G has a non-trivial irreducible p-Brauer character which is rational valued. The first author is partially supported by the Ministerio de Educación y Ciencia proyecto MTM2004-06067-C02-01, while the second gratefully acknowledges the support of the NSA (grant H98230-04-0066).