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<b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">G</font> be  <a href="group_1.html#V1">strict</a> <a href="group_1.html#NM1">Group</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:18"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">G</font> is <a href="group_1.html#V6">finite</a>
 <b>and </b><br/><a NAME="E2:18"/><i><font color="Green">E47</font></i>: 
 <a href="group_1.html#K9">ord</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 <b>and </b><br/><a NAME="E3:18"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">p</font> is <a href="int_2.html#V1">prime</a>
 ;<br/>

<b>let </b><font color="Maroon">H</font> be  <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/>

<a NAME="E4:18"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">H</font> is <a href="group_1.html#V6">finite</a>
 
<b>by </b><i>, <a class="ref" href="group_2.html#T48">GROUP_2:48</a></i>;<br/>
<a NAME="E5:18"/>
 <a href="group_1.html#K9">ord</a> <font color="Maroon">H</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">p</font>
 
<b>by </b><i>, , <a class="ref" href="group_2.html#T178">GROUP_2:178</a></i>;<br/>
<a NAME="E6:18"/><b>then </b>
(  <a href="group_1.html#K9">ord</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> 1 or  <a href="group_1.html#K9">ord</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> )
 
<b>by </b><i>, <a class="ref" href="int_2.html#D5">INT_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E7:18"/>
( <font color="Maroon">H</font> <a href="group_2.html#R1">=</a>  <a href="group_2.html#K5">(1).</a> <font color="Maroon">G</font> or <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> )
 <b>by </b><i>, , , <a class="ref" href="group_2.html#T82">GROUP_2:82</a>, <a class="ref" href="group_2.html#T85">GROUP_2:85</a></i>;<br/>


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