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

Returns cyclic factors and their orders from the Smith normal form.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := AbelianGroupCyclicFactors(g);</pre>

<p>

<table>
<tr>
<td>group</td>
<td><pre>  g  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>list of cyclic factors of g</td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Returns a list of lists of cyclic factors of the group
and the orders of the cyclic factors obtained from the Smith normal
form of the relations for g.


<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute the cyclic factors of a ray class group: 
<pre>

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

kash> g := RayClassGroupToAbelianGroup(3*O, [1, 2]);
RayClassGroupToAbelianGroup(<3>, [ 1, 2 ])
Group with relations:
[4 0]
[0 2]
kash> L := AbelianGroupCyclicFactors(g);
> [ [ <2, [0, 1]>, 2 ], [ <[1, -3]>, 4 ] ]

</pre>

<p>


<hr>

<p>
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