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January 16th, 2018, 01:12 AM   #1
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Proving that $Gal(L/F)\overset{∼}{=}N_G(H)/H$

Please help me to answer this problem:

Let $F \subset E$ be a Galois extension and $L$ be a subfield of $E$ containing $F$. Let $G= Gal(E/F)$ and $H =Gal(E/L)$.

Show that $Gal(L/F)\overset{∼}{=}N_G(H)/H$.(Note that this is a generalization of one part of the FTGT, which adresses the case where $H ⊴ G$)

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