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Let $\mathbf{F}_q$ ($q=p^f$) be a finite field. We are interested in the characters $\chi: \mathbf{F}_q\rightarrow \mathbf{K}$ ($\chi(0)=0$) where the $ \mathbf{K}$ is an alg.closed field of ...

Denote the symmetric group of order $n!$ by $S_n$. Let $H:=S_p$ for an odd prime $p$. Every finite field $k$ is a splitting field $(^*)$ for $kH$, in particular $k:=\mathbb{F}_p$. Questions: Is $k:=\...