Theorem 11.2. There is a bijection

\begin{array}{l} {\begin{array}{c} finite subgroups \\ Δ \subset K^{*} ∕ {(K^{*})}^{n} \end{array}} & \leftrightarrow {\begin{array}{c} finite abelian extension L ∕ K \\ of exponent dividing n \end{array}} \\ Δ & \mapsto K (\sqrt[n]{Δ}) \\ \frac{{(L^{*})}^{n} \cap K^{*}}{{(K^{*})}^{n}} & \leftarrow ↤ L \end{array}