Fields generated by characters of finite linear groups
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classification
math.NT
math.GRmath.RT
keywords
groupsfieldsfinitegeneratedleftlinearmathbbmathrm
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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 $\mathrm{SL}_2\left(\mathbb{F}_q\right)$.
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