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<div><span class="kw">theorem </span><a NAME="T21"><span class="comment"><font color="firebrick">:: GROUP_22:21</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">phi</font> being   <a href="group_22.html#NM2" title="GROUP_22:NM.2">Automorphism</a> of <font color="Olive" title="b1">G</font>  st <font color="Olive" title="b1">G</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  holds <br/> for <font color="Olive" title="b3">p</font> being   <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b4">P</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</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">P</font> <a href="group_10.html#R3" title="GROUP_10:pred.3">is_Sylow_p-subgroup_of_prime</a> <font color="Olive" title="b3">p</font> holds <br/> <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">phi</font> <a href="grsolv_1.html#K1" title="GRSOLV_1:func.1">|</a> <font color="Olive" title="b4">P</font></span>)</span> <a href="group_10.html#R3" title="GROUP_10:pred.3">is_Sylow_p-subgroup_of_prime</a> <font color="Olive" title="b3">p</font></div></div>
