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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:126"/>
(  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="group_2.html#K12" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="group_2.html#K13" target="_self">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="group_2.html#T132" target="_self">Th132</a></i>;<br/>
<b>hence </b><a NAME="E2:126"/>
(  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K14" target="_self">Left_Cosets</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K15" target="_self">Right_Cosets</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="group_2.html#D15" target="_self">Def15</a>, <a class="ref" href="group_2.html#D16" target="_self">Def16</a></i>;<br/>


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