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Rational irreducible characters and rational conjugacy classes in finite groups |
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| Authors: | Gabriel Navarro Pham Huu Tiep |
| Institution: | Facultat de Matemàtiques, Universitat de València, Burjassot, València 46100, Spain ; Department of Mathematics, University of Florida, Gainesville, Florida 32611 |
| Abstract: | We prove that a finite group  has two rational-valued irreducible characters if and only if it has two rational conjugacy classes, and determine the structure of any such group. Along the way we also prove a conjecture of Gow stating that any finite group of even order has a non-trivial rational-valued irreducible character of odd degree. |
| Keywords: | Rational irreducible character rational conjugacy class |
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