Algebraic Number Theory
《Algebraic Number Theory》 · 第 363 页 · Chapter VI，Section 1「Ideles and Idele Classes」，Definition 1.7
The group $C_K^{\mathfrak m}=I_K^{\mathfrak m}K^*/K^*$, formed from the idele group $I_K^{\mathfrak m}=\prod_{\mathfrak p}U_{\mathfrak p}^{(n_{\mathfrak p})}$, is called the congruence subgroup mod $\mathfrak m$, and the quotient group $C_K/C_K^{\mathfrak m}$ is called the ray class group mod $\mathfrak m$.