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<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: GROUP_24:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">A</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b3">phi</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Olive" title="b2">A</font>,<span class="p1">(<span class="default"><a href="autgroup.html#K3" title="AUTGROUP:func.3">AutGroup</a> <font color="Olive" title="b1">G</font></span>)</span> holds  <span class="p1">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <span class="p2">(<span class="default"><a href="group_24.html#K2" title="GROUP_24:func.2">incl1</a> (<font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">phi</font>)</span>)</span></span>)</span> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <span class="p1">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <span class="p2">(<span class="default"><a href="group_24.html#K3" title="GROUP_24:func.3">incl2</a> (<font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">phi</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_24.html#K1" title="GROUP_24:func.1">semidirect_product</a> (<font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">phi</font>)</div></div>
