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تسجيل مستخدم جديدFields generated by characters of finite linear groups
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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 $mathrm{GL}_mleft(mathbb{F}_qright)$ and $mathrm{SL}_2left(mathbb{F}_qright)$.
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For a finite group $G$, let $K(G)$ denote the field generated over $mathbb{Q}$ by its character values. For $n>24$, G. R. Robinson and J. G. Thompson proved that $$K(A_n)=mathbb{Q}left ({ sqrt{p^*} : pleq n {text{ an odd prime with } p eq n-2}}rig
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