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

Returns the direct product of two finite abelian groups.

<p><p>

<h3>
Syntax:
</h3>
<pre>d := AbelianGroupDirectProduct(g1, g2);
d := AbelianGroupDirectProduct(L);</pre>

<p>

<table>
<tr>
<td>groups</td>
<td><pre>  g1, g2, d  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>list of groups</td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
In the first case the direct product d of the group g1 and the
group g2 is computed. In the second case the direct product
d of all groups in the list is computed.
Instead of using <tt>AbelianGroupDirectProduct</tt> you may
use the * operator (see example).


<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute the direct product using AbelianGroupDirectProduct: 
<pre>

kash> g1 := AbelianGroupCreate([[5]]);
Group with relations:
[5]
kash> g2 := AbelianGroupCreate([[7,7],[6,8]]);
Group with relations:
[7 7]
[6 8]
kash> d := AbelianGroupDirectProduct([g1, g2]);
Group with relations:
[5 0 0]
[0 7 7]
[0 6 8]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 Compute the direct product using *: 
<pre>

kash> d := g1*g2;
Group with relations:
[5 0 0]
[0 7 7]
[0 6 8]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 Compute the power \bigoplus_{i = 1}^{4}g_{1}: 
<pre>

kash> p := g1^4;
> Group with relations:
[5 0 0 0]
[0 5 0 0]
[0 0 5 0]
[0 0 0 5]

</pre>

<p>


<hr>

<p>
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