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<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">H</font> be  <a href="group_1.html#V1">strict</a> <a href="group_1.html#NM1">Group</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:100"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">G</font>,<font color="Maroon">H</font> <a href="group_6.html#R1" target="_self">are_isomorphic</a> 
 <b>and </b><br/><a NAME="E2:100"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">G</font> is  <a href="group_1.html#V7">commutative</a> <a href="group_1.html#NM1">Group</a>
 ;<br/>

<b>consider </b><font color="Maroon">h</font> being   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">G</font>,<font color="Maroon">H</font><b> such that </b><br/><a NAME="E4:100"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">h</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 <b>by </b><i>, </i>;<br/>
<a NAME="E5:100"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">h</font> <a href="group_6.html#NR2" target="_self">is_epimorphism</a> 
 
<b>by </b><i>, <a class="ref" href="group_6.html#T8" target="_self">Th8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="100_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>, <font color="Maroon">d</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>;<br/><b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E2:100_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="group_6.html#T6" target="_self">Th6</a></i>;<br/><b>consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E4:100_1"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 <b>by </b><i>, <a class="ref" href="group_6.html#T6" target="_self">Th6</a></i>;<br/><b>thus </b><font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">d</font> = 
<font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i>, <a class="ref" href="group_6.html#D2" target="_self">Def2</a>, </i>
<br/>.= 
<font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">d</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font>
<b>by </b><i>, <a class="ref" href="group_6.html#D2" target="_self">Def2</a>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:100"/>
<font color="Maroon">H</font> is  <a href="group_1.html#V7">commutative</a> <a href="group_1.html#NM1">Group</a>
 <b>by </b><i><a class="ref" href="group_1.html#D16">GROUP_1:def 16</a></i>;<br/>


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