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

Returns the group consisting of homomorphisms between two groups.

<p><p>

<h3>
Syntax:
</h3>
<pre>h := AbelianHomGroup(g1, g2);</pre>

<p>

<table>
<tr>
<td>groups</td>
<td><pre>  g1, g2, h  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Returns the group h consisting of homomorphisms from
g_1 to g_2.

<p><p>

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

<pre>

kash> g1 := AbelianGroupCreate([[1,2,3],[2,4,0], [2,0,0]]);;
kash> g2 := AbelianGroupCreate([[1,0,0],[0,4,0], [1,1,1]]);;
kash> h := AbelianHomGroup(g1, g2);
Group with relations:
[2 0]
[0 4]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 <tt>elt</tt> is an element of h: 
<pre>

kash> elt := AbelianGroupEltCreate(h, [0,1]);
[0 1]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 <tt>hom</tt> is a homomorphism from <tt>g1</tt> to <tt>g2</tt>: 
<pre>

kash> hom := AbelianGroupDiscreteExp(elt);
HomMatrix =
[ 0  0  0]
[ 0  3  0]
[ 0 -2  0] 
from Group with relations:
[1 2 3]
[2 4 0]
[2 0 0] 
to Group with relations:
[1 0 0]
[0 4 0]
[1 1 1]

kash> elt1 := AbelianGroupEltCreate(g1, [1,1,0]);
[1 1 0]
kash> elt2 := hom*elt1;
> [0 3 0]

</pre>

<p>


<hr>

<p>
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