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

Creates a subgroup.

<p><p>

<h3>
Syntax:
</h3>
<pre>s := AbelianSubGroup([g,] L [, generators]);
s := AbelianSubGroup(g, mat [, generators]);</pre>

<p>

<table>
<tr>
<td>groups</td>
<td><pre>  g, s  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>list of elements of g or list of exponent vectors</td>
</tr>
<tr>
<td>matrix</td>
<td><pre>  mat  </pre></td>
<td></td>
</tr>
<tr>
<td>boolean</td>
<td><pre>  generators  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Creates a subgroup s of the group g. The subgroup s is
generated by the elements of the list <tt>L</tt>.
If you use <tt>s := AbelianSubGroup(g, mat);</tt>
then the subgroup s
is generated by the elements represented by the rows of
<tt>mat</tt>. If the last (optional) parameter <tt>generators</tt>
is <tt>true</tt> then the new generators are computed, too.


<p><p>

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

<pre>

kash> g := AbelianGroupCreate([[0,1,2],[5,6,0],[0,4,5]]);;


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 Create subgroup with list of exponent vectors: 
<pre>

kash> s := AbelianSubGroup(g, [[0,1,0], [0,0,5]]);
Group with relations:
[1 1]
[0 3]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 Create subgroup with list of group elements: 
<pre>

kash> elt1 := AbelianGroupEltCreate(g, [0,1,0]);;
kash> elt2 := AbelianGroupEltCreate(g, [0,0,5]);;
kash> s := AbelianSubGroup([elt1, elt2]);
Group with relations:
[1 1]
[0 3]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 Create subgroup with matrix: 
<pre>

kash> mat := Mat(Z, [[0,1,0], [0,0,5]]);;
kash> s := AbelianSubGroup(g, mat);
> Group with relations:
[1 1]
[0 3]

</pre>

<p>


<hr>

<p>
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