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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E14">Def13</font></span>   defines <a href="group_9.html#V6" title="GROUP_9:attr.6">simple</a> <a onclick="hs(this)" href="javascript:()">GROUP_9:def 13 : <br/></a><span> for <font color="Olive" title="b1">O</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">IT</font> being   <a href="group_9.html#NM1" title="GROUP_9:NM.1">GroupWithOperators</a> of <font color="Olive" title="b1">O</font> holds <br/> ( <font color="Olive" title="b2">IT</font> is  <a href="group_9.html#V6" title="GROUP_9:attr.6">simple</a>  iff (  not <font color="Olive" title="b2">IT</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  &amp; (  for <font color="Olive" title="b3">H</font> being   <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a>   <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>   <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b2">IT</font>  holds <br/>(  not <font color="Olive" title="b3">H</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="group_9.html#K5" title="GROUP_9:func.5">(Omega).</a> <font color="Olive" title="b2">IT</font> or  not <font color="Olive" title="b3">H</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="group_9.html#K4" title="GROUP_9:func.4">(1).</a> <font color="Olive" title="b2">IT</font> ) ) ) );<br/></span></div>
