Rational irreducible characters and rational conjugacy classes in finite groups

Navarro, Gabriel; Tiep, Pham

doi:10.1090/S0002-9947-07-04375-9

Rational irreducible characters and rational conjugacy classes in finite groups
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by Gabriel Navarro and Pham Huu Tiep PDF

Trans. Amer. Math. Soc. 360 (2008), 2443-2465 Request permission

Abstract:

We prove that a finite group $G$ 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.

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