Galois Action and Localization in Number Fields

Jim Coykendall, Jared Kettinger

For a Galois number field $K$, the Galois group $\text{Gal}(K/\mathbb{Q})$ acts on the class group ${\text{Cl}}_K$ in a very natural way: $\ddot{I}ƒ\cdot [I]=[\ddot{I}ƒ(I)]$ for any $σ\in \text{Ga…