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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">H1</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">H2</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">H3</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">H4</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/>









<b>assume </b><a NAME="E1:71"/>
( <font color="Maroon">H1</font> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">H2</font> &amp; <font color="Maroon">H3</font> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">H4</font> )
 ;<br/>

<a NAME="E2:71"/><b>then </b>
 <a href="group_5.html#K5" target="_self">commutators</a> <font color="Maroon">H1</font>,<font color="Maroon">H3</font> <a href="tarski.html#R1">c=</a>  <a href="group_5.html#K5" target="_self">commutators</a> <font color="Maroon">H2</font>,<font color="Maroon">H4</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:71"/><b>then </b>
 <a href="group_4.html#K5">gr</a> <span class="p1">(<span class="default"><a href="group_5.html#K5" target="_self">commutators</a> <font color="Maroon">H1</font>,<font color="Maroon">H3</font></span>)</span> is    <a href="group_2.html#M1">Subgroup</a> of  <a href="group_4.html#K5">gr</a> <span class="p1">(<span class="default"><a href="group_5.html#K5" target="_self">commutators</a> <font color="Maroon">H2</font>,<font color="Maroon">H4</font></span>)</span>
 
<b>by </b><i><a class="ref" href="group_4.html#T41">GROUP_4:41</a></i>;<br/>
<a NAME="E4:71"/><b>then </b>
<span class="p1"><a href="group_5.html#K8" target="_self">[.</a><span class="default"><font color="Maroon">H1</font>,<font color="Maroon">H3</font></span><a href="group_5.html#K8" target="_self">.]</a></span> is    <a href="group_2.html#M1">Subgroup</a> of  <a href="group_4.html#K5">gr</a> <span class="p1">(<span class="default"><a href="group_5.html#K5" target="_self">commutators</a> <font color="Maroon">H2</font>,<font color="Maroon">H4</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E5:71"/>
<span class="p1"><a href="group_5.html#K8" target="_self">[.</a><span class="default"><font color="Maroon">H1</font>,<font color="Maroon">H3</font></span><a href="group_5.html#K8" target="_self">.]</a></span> is    <a href="group_2.html#M1">Subgroup</a> of <span class="p1"><a href="group_5.html#K8" target="_self">[.</a><span class="default"><font color="Maroon">H2</font>,<font color="Maroon">H4</font></span><a href="group_5.html#K8" target="_self">.]</a></span>
 ;<br/>


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