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    Kronecker--Weber theorem

    T-QX5QU

    Every finite abelian extension of $\QQ$ lies inside a cyclotomic field.Suggest a slogan

    Let \(K\subseteq\CC\) be a finite Galois extension of \(\QQ\) with \(\Gal(K/\QQ)\) abelian. Then there is an integer \(m\geq 1\) such that \(K \subseteq \QQ(\zeta_m)\), where \(\zeta_m\coloneqq e^{2\pi i/m}\).

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