Odd-degree rational characters and the order of rational elements in finite groups

TL;DR

This paper proves that in finite groups, if all rational irreducible characters have odd degree, then all rational elements are 2-elements, confirming a conjecture by Tiep and Tong-Viet.

Contribution

The paper confirms a conjecture linking rational character degrees to the order of rational elements in finite groups.

Findings

Rational irreducible characters of odd degree imply rational elements are 2-elements.

The conjecture by Tiep and Tong-Viet is validated.

Provides new insight into the structure of finite groups based on character theory.

Abstract

We prove that, in a finite group, if every rational irreducible character has odd degree, then all rational elements are 2-elements, as it was originally conjectured by Tiep and Tong-Viet.