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In terms of the Galois correspondence, a transitive group $G\leq S_n$ is the Galois group of an irreducible degree $n$ polynomial $f(x)\in K[x]$. Let $F=K(\alpha)$ where $\alpha$ is a root of $f(x)$. Then the subfields are intermediate fields for the extension $F/K$.

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• Review status: reviewed
• Last edited by John Jones on 2018-07-09 22:54:29
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