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<div><span class="kw">theorem </span><a NAME="T54"><span class="comment"><font color="firebrick">:: GROUP_5:54</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b2">H</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G</font> holds <br/> (  <a href="group_5.html#K5" title="GROUP_5:func.5">commutators</a> (<span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(1).</a> <font color="Olive" title="b1">G</font></span>)</span>,<font color="Olive" title="b2">H</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Olive" title="b1">G</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  <a href="group_5.html#K5" title="GROUP_5:func.5">commutators</a> (<font color="Olive" title="b2">H</font>,<span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(1).</a> <font color="Olive" title="b1">G</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Olive" title="b1">G</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )</div></div>
