One of the main theorems in class field theory is that there is a bijection between the finite-index open subgroups of the idele class group of a number field field $K$ and the abelian extensions of $K$. I was wondering where I could find examples and explicit computations of such abelian extensions from finite open subgroups of $\mathbb{I}_K$.
2026-03-25 11:16:06.1774437366
Examples of Finite-index Open Subgroups of Idele Class Group
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