Then there exists a unique unramified $L∕K$ of degree $n$. Moreover, $L∕K$ is Galois and the natural $\mathrm{Gal}(L∕K)\to \mathrm{Gal}(k_L∕k)$ is an isomorphism. In particular, $\mathrm{Gal}(L∕K)\cong ⟨{\mathrm{Frob}}_{L∕K}⟩$ is cyclic, where ${\mathrm{Frob}}_{L∕K}(x)=x^{q}mod{m}_L$ for all $x\in O_L$.