ray class group

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

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$\mathbb{I}^{\mathfrak{m}}$ is the subgroup of the ideal group of $K$ generated by all prime ideals which do not occur in the factorization of ${\mathfrak{m}}$ .
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$K_{{\mathfrak{m}},1}$ is the subgroup of $\mathbb{I}^{\mathfrak{m}}$ consisting of all principal ideals in the ring of integers of $K$ having the form $(\alpha)$ where $\alpha$ is multiplicatively congruent to $1\bmod{\mathfrak{m}}$ .

Title	ray class group
Canonical name	RayClassGroup
Date of creation	2013-03-22 12:50:19
Last modified on	2013-03-22 12:50:19
Owner	djao (24)
Last modified by	djao (24)
Numerical id	4
Author	djao (24)
Entry type	Definition
Classification	msc 11R29