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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E51">Th49</font></span>: <a NAME="T52"><span class="comment"><font color="firebrick">:: GROUP_24:52</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><br/>  for <font color="Olive" title="b3">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> holds <br/> ( <font color="Olive" title="b2">H</font>,<font color="Olive" title="b3">N</font> <a href="group_24.html#R1" title="GROUP_24:pred.1">are_complements_in</a> <font color="Olive" title="b1">G</font> iff ( <font color="Olive" title="b2">H</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Olive" title="b3">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">G</font>, the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Olive" title="b1">G</font> #) &amp; <font color="Olive" title="b2">H</font> <a href="group_6.html#K2" title="GROUP_6:func.2">/\</a> <font color="Olive" title="b3">N</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a>  <a href="group_2.html#K6" title="GROUP_2:func.6">(1).</a> <font color="Olive" title="b1">G</font> ) )</div></div>
