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<b>let </b><font color="Maroon" title="c1">p</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F</font>, <font color="Olive" title="b2">G</font> being <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>  st  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> &amp;  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Olive" title="b2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Maroon" title="c1">p</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> holds <br/><font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">G</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/><b>let </b><font color="Maroon" title="c2">F</font>, <font color="Maroon" title="c3">G</font> be  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> &amp;  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Maroon" title="c1">p</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> implies <font color="Maroon" title="c2">F</font>,<font color="Maroon" title="c3">G</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a>  )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:19"/><i><font color="Green" title="E17">A1</font></i>: 
 <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font>
 <b>and </b><br/><a NAME="E2:19"/><i><font color="Green" title="E18">A2</font></i>: 
 <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Maroon" title="c3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font>
 <b>and </b><br/><a NAME="E3:19"/><i><font color="Green" title="E19">A3</font></i>: 
<font color="Maroon" title="c1">p</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">F</font>,<font color="Maroon" title="c3">G</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/>

<a NAME="E4:19"/><i><font color="Green" title="E20">A4</font></i>: 
<font color="Maroon" title="c2">F</font> is  <a href="gr_cy_1.html#V1" title="GR_CY_1:attr.1">cyclic</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>
 
<b>by </b><i><a class="txt" href="#E1:19"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="#E3:19"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="gr_cy_1.html#T45" title="GR_CY_1:th.45">GR_CY_1:45</a></i>;<br/>
<a NAME="E5:19"/>
<font color="Maroon" title="c3">G</font> is  <a href="gr_cy_1.html#V1" title="GR_CY_1:attr.1">cyclic</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>
 
<b>by </b><i><a class="txt" href="#E2:19"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="#E3:19"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="gr_cy_1.html#T45" title="GR_CY_1:th.45">GR_CY_1:45</a></i>;<br/>
<b>hence </b><a NAME="E6:19"/>
<font color="Maroon" title="c2">F</font>,<font color="Maroon" title="c3">G</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> 
 <b>by </b><i><a class="txt" href="#E1:19"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="#E2:19"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="#E4:19"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="gr_cy_2.html#T23" target="_self" title="GR_CY_2:th.23">Th23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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