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Let $K$ be a field such that for every finite extension $L$ of $K$ and for every natural number $n>0$ the index $[L^*:(L^*)^n]$ is finite and, if $char(K)=p>0$ and $f: L \\to L$ is given by $f(x)=x^p-x$, the index $[L^+:f[L]]$ is also finite. 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