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

Creates the dual homomorphism of a given homomorphism between two
finite Abelian groups.

<p><p>

<h3>
Syntax:
</h3>
<pre>dualhom := AbelianDualHom(hom);
</pre>

<p>

<table>
<tr>
<td>homomorphism</td>
<td><pre>  hom  </pre></td>
<td>homomorphism from g1 to g2</td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Creates the dual homomorphism from the group g2^{*}
to group g1^{*} of a homomorphism hom: g1 \to g2.
The dual homomorphism is defined by:
hom^{*}:g2^{*}rightarrow g1^{*}
and hom^{*}: chi rightarrow chi * hom.


<p><p>

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

<pre>

kash> g1 := AbelianGroupCreate([[0,1,2],[5,6,0],[0,4,5]]);;
kash> g2 := AbelianGroupCreate([[0,2],[3,0]]);;
kash> mat := Mat(Z, [[-24,24],[20,-20],[-10,10]]);;
kash> hom := AbelianGroupHomCreate(g1, g2, mat, true);
HomMatrix =
[-24  24]
[ 20 -20]
[-10  10] 
from Group with relations:
[0 1 2]
[5 6 0]
[0 4 5] 
to Group with relations:
[0 2]
[3 0]

kash> dualhom:=AbelianDualHom(hom);
HomMatrix =
[5] 
from Group with relations:
[6] 
to Group with relations:
[15]


</pre>

<p>


<hr>

<p>
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