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Let $K$ be an extension field of $F$. A \emph{Galois closure} of $K/F$ is a field $L \supseteq K$ that is a Galois extension of $F$ and is minimal in that respect, i.e. no proper subfield of $L$ containing $K$ is normal over $F$.
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Let $K$ be an extension field of $F$. A Galois closure of $K/F$ is a field $L \supseteq K$ that is a Galois extension of $F$ and is minimal in that respect, i.e. no proper subfield of $L$ containing $K$ is normal over $F$.
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