ray class group
Let $\U0001d52a$ be a modulus^{} for a number field $K$. The ray class group of $K$ mod $\U0001d52a$ is the group ${\mathbb{I}}^{\U0001d52a}/{K}_{\U0001d52a,1}$, where

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${\mathbb{I}}^{\U0001d52a}$ is the subgroup of the ideal group of $K$ generated by all prime ideals^{} which do not occur in the factorization of $\U0001d52a$.

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${K}_{\U0001d52a,1}$ is the subgroup of ${\mathbb{I}}^{\U0001d52a}$ consisting of all principal ideals^{} in the ring of integers^{} of $K$ having the form $(\alpha )$ where $\alpha $ is multiplicatively congruent to $1mod\U0001d52a$.
Title  ray class group 

Canonical name  RayClassGroup 
Date of creation  20130322 12:50:19 
Last modified on  20130322 12:50:19 
Owner  djao (24) 
Last modified by  djao (24) 
Numerical id  4 
Author  djao (24) 
Entry type  Definition 
Classification  msc 11R29 