On a question by G. Navarro on the character field generation of odd-degree characters

Abstract

In [Publ. Mat. 67 (2023), no. 1, 173-198], G. Navarro asked whether the character field of an odd-degree character of a finite group is generated by a single character value. We show by explicit examples that the answer is negative in general.

Expanded and revised version, with additional results, examples, and computational data