Ray class group
= Ray class group
{title2=$\operatorname{Cl}_{\mathfrak m}(K)$}
{wiki}
The ray class group modulo $\mathfrak m$ is $I_K(\mathfrak m)/P_K(\mathfrak m)$, where the numerator consists of fractional ideals prime to $\mathfrak m_0$ and the denominator consists of $(\alpha)$ with $\alpha\equiv1$ at the finite modulus and positive at every real place in $\mathfrak m_\infty$.