Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 123 / 1 / b

Let $I_K(\mathfrak{m})$ be the group of fractional ideals prime to ${\mathfrak{m}}_0$. Let $P_K(\mathfrak{m})$ consist of principal ideals $(\alpha )$ withfor every $\mathfrak{p}\mid {\mathfrak{m}}_0$ and $\sigma (\alpha )>0$ for every real place $\sigma \mid {\mathfrak{m}}_{\infty }$. The ray class group is