Fields generated by characters of finite linear groups

Madeline Locus Dawsey, Ken Ono, Ian Wagner

Published 2019-12-15Version 1

In previous work, the authors confirmed the speculation of J. G. Thompson that certain multiquadratic fields are generated by specified character values of sufficiently large alternating groups $A_n$. Here we address the natural generalization of this speculation to the finite general linear groups $\mathrm{GL}_m\left(\mathbb{F}_q\right)$ and $\mathrm{SL}_2\left(\mathbb{F}_q\right)$.