For $d\in\mathbb{Q}$, how could one show that $Q(\sqrt{d})$ lies in a cyclotomic extension of $\mathbb{Q}$ without using the Kronecker-Weber theorem?
Cyclotomic extension over Q special case of Kronecker Weber theorem.
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galois-theory
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1@rayjsh: It appears you tried to edit your own question, but were not logged in-the edit comes from an anonymous user. If you log in, I think you should be able to edit it. I wouldn't want to put those words in your mouth if they aren't yours. – 2012-04-18