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 rationalvalued irreducible character of odd degree.
- Rational conjugacy class
- Rational irreducible character
ASJC Scopus subject areas
- Applied Mathematics