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<div>:: <span class="kw">deftheorem </span>   defines <a href="group_24.html#R1" title="GROUP_24:pred.1">are_complements_in</a> <a onclick="hs(this)" href="javascript:()">GROUP_24:def 5 : <br/></a><span> 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>, <font color="Olive" title="b3">N</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/> ( <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="b3">N</font> is  <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>  &amp; <font color="Olive" title="b2">H</font> <a href="group_4.html#K7" title="GROUP_4:func.7">*</a> <font color="Olive" title="b3">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">G</font> &amp; <font color="Olive" title="b2">H</font> <a href="group_2.html#K10" title="GROUP_2:func.10">/\</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> ) );<br/></span></div>
