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<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: GROUP_24:51</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">K</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b3">H</font> being    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Olive" title="b2">K</font><br/>  for <font color="Olive" title="b4">N</font> being   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G</font>  st <font color="Olive" title="b4">N</font> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Olive" title="b2">K</font> holds <br/>( <font color="Olive" title="b3">H</font>,<font color="Olive" title="b4">N</font> <a href="group_24.html#R1" title="GROUP_24:pred.1">are_complements_in</a> <font color="Olive" title="b2">K</font> iff <font color="Olive" title="b3">H</font>,(<font color="Olive" title="b2">K</font>,<font color="Olive" title="b4">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a>  <a href="group_24.html#R1" title="GROUP_24:pred.1">are_complements_in</a> <font color="Olive" title="b2">K</font> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="group_24.html#T50" target="_self" onmouseover="rs('group_24/T50')" onmouseout="rh()">Th46</a></span>;<br/></div></div>
