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Let $K$ be a finite normal extension of $F$ such that there are no proper intermediate extensions of $K/F$. Show that $[K:F]$ is prime. Give a conterexample if $K$ is not normal over $F$.

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    Do you know some about Galois correspondance ?2012-02-12
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    @Lierre: the Galois correspondence is not necessary here. You can prove it just starting from the definition of $[K:F]$.2012-02-12
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    @DamianSobota: Maybe (although I don't see any immediate solution without it) ! But if it is an exercise, we should guess what is the expected proof. That's why I asked.2012-02-12
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    @Damian: really? This is quite amazing: could you please elaborate?2012-02-12

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