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February 1st, 2018, 02:46 AM  #1 
Senior Member Joined: Jan 2015 From: usa Posts: 104 Thanks: 1  Cyclic normal group
Please help me to prove the following problem: Let $f\subset E$ be a Galois extension and assume that $E=F(\alpha)$ with $\alpha^n\in F$. Let $G=Gal(E/F)$. Show that $G$ has a cyclic normal subgroup $N$ of order dividing $n$ such that $G/N$ is abelian and has order dividing $\phi(n)$. Thanks. Last edited by skipjack; June 24th, 2018 at 08:21 AM. 

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cyclic, group, normal 
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