Year: 2026
Type: preprint
Abstract: For a finite group $G$, define the field $\mathbb{Q}(G) := \mathbb{Q}(\{χ(g) : χ\in \operatorname{Irr}(G) , g \in G\})$. In this article we compute generating sets for the fields $\mathbb{Q}(G)$ when $G$ is a finite general or special linear group, a finite general or special unitary group, or one of the simple groups $\operatorname{PSL}_n(q)$ or $\operatorname{PSU}_n(q)$. We then apply these results to classify all number fields $F$ of degree $2$ or $3$ over $\mathbb{Q}$ such that $F = \mathbb{Q}(S)$ for some non-abelian simple group $S$.
Source: arXiv (Cornell University)
Author: Ketchum, Eden
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7214802166