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Sep 17, 2019 at 17:29 vote accept seoneo
Sep 10, 2019 at 23:36 comment added GH from MO @seoneo: If $L/F$ is abelian, then any intermediate field extension is Galois over $F$. This forces that $L=F(\alpha)=K(\alpha)$, hence $L=M$.
Sep 10, 2019 at 16:36 comment added seoneo Ahhhh I ment G(L/F) abelian... But yours is a nice ce.
Sep 10, 2019 at 9:25 history answered GH from MO CC BY-SA 4.0