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

Tests whether the Ray Class Field defined by the given data
will be a central extension.

<p><p>

<h3>
Syntax:
</h3>
<pre>flag := RayClassFieldIsCentral(G [, l]);</pre>

<p>

<table>
<tr>
<td>boolean</td>
<td><pre>  flag  </pre></td>
<td></td>
</tr>
<tr>
<td>AbelianGroup</td>
<td><pre>  G  </pre></td>
<td>a quotient from RayClassGroupToAbelianGroup</td>
</tr>
<tr>
<td>list</td>
<td><pre>  l  </pre></td>
<td>of automorphisms, if not present all known automorphisms are used.</td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
<i>no detailed description available yet</i>

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
We'll investigate the ray class field mod m := (6)\p|1^\infty\p|2^\infty in k := Q(\sqrt{10}):
<pre>

kash> o := OrderMaximal(Z, 2, 10);
Generating polynomial: x^2 - 10
Discriminant: 40 

kash> OrderAutomorphisms(o);
[ [0, 1], [0, -1] ]
kash> G1 := RayClassGroupToAbelianGroup(6*o, [1, 2]);
RayClassGroupToAbelianGroup(<6>, [ 1, 2 ])
Group with relations:
[2 0 0]
[0 4 0]
[0 0 2]
kash> rcg := FindMaximalCentralField(G1);
[2 0 0]
[0 2 0]
[0 0 2]
[0 0 0]
[0 0 0]
[0 0 0]
kash> G2 := AbelianQuotientGroup(G1, AbelianSubGroup(G1, rcg));
Group with relations:
[2 0 0]
[0 2 0]
[0 0 2]
[0 0 0]
[0 0 0]
[0 0 0]
[2 0 0]
[0 4 0]
[0 0 2]
kash> RayClassFieldIsCentral(G1);
false
kash> RayClassFieldIsCentral(G2);
> true

</pre>

<p>


<hr>

<p>
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