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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="AbelianRayGroupImbed"></a>
AbelianRayGroupImbed
</h2>

Imbeds a ClassGroup into a RayClassGroup.

<p><p>

<h3>
Syntax:
</h3>
<pre>dualhom := AbelianRayGroupImbed(G,g);
</pre>

<p>

<table>
<tr>
<td>abstract rayclassgroup</td>
<td><pre>  G  </pre></td>
<td></td>
</tr>
<tr>
<td>abstract classgroup</td>
<td><pre>  g  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#RayClassGroupToAbelianGroup">RayClassGroupToAbelianGroup</a>

<p>

<h3>
Description:
</h3>
If I^{({ \goth f})}/P_{ \goth f} is a ray class group with
conductor { \goth f} and I^{ \goth f'}/U_{ \goth f'} is
a classgroup with conductor {\goth f'}, then we may
imbed U_{\goth f'} canonically into
I^{({\goth f})}/P_{\goth f}: U_{\goth f'}^{({\goth f})}/P_{\goth f}
is a subgroup of I^{({\goth f})}/P_{\goth f}.




<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>

<pre>

kash> O:=OrderMaximal(x^3-x^2-9*x+8);;
kash> G :=RayClassGroupToAbelianGroup(25*O);;
kash> g:=RayClassGroupToAbelianGroup(1*O);;
kash> u:=AbelianRayGroupImbed(G,g);
Group with relations:
[2 0]
[0 5]


</pre>

<p>


<hr>

<p>
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