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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">N</font> be  <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="Maroon" title="c2">G</font>;<br/><b>assume </b><a NAME="E1:58_1_1_1"/><i><font color="Green" title="E38">A1</font></i>: 
<font color="Maroon" title="c5">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_9.html#K13" title="GROUP_9:func.13">Ker</a> <font color="Maroon" title="c4">g</font></span>)</span>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><a href="group_9.html#K13" title="GROUP_9:func.13">Ker</a> <font color="Maroon" title="c4">g</font></span>)</span> #)
 ;<br/><b>reconsider </b><font color="Maroon" title="c6">G'</font> = <font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c7">H'</font> = <font color="Maroon" title="c3">H</font> as   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a> ;<br/><b>reconsider </b><font color="Maroon" title="c8">g'</font> = <font color="Maroon" title="c4">g</font> as   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c6">G'</font>,<font color="Maroon" title="c7">H'</font> ;<br/><a NAME="E4:58_1_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Ker</a> <font color="Maroon" title="c8">g'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font> : <font color="Maroon" title="c4">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c3">H</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="group_6.html#D10" title="GROUP_6:def.10">GROUP_6:def 10</a></i>;<br/><a NAME="E5:58_1_1_1"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Ker</a> <font color="Maroon" title="c8">g'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">N</font>
 <b>by </b><i><a class="txt" href="group_9.html#E1:58_1_1_1"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="group_9.html#D24" target="_self" title="GROUP_9:def.24">Def24</a></i>;<br/><b>hence </b><a NAME="E6:58_1_1_1"/>
<font color="Maroon" title="c5">N</font> is <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>
 <b>by </b><i><a class="ref" href="group_2.html#T68" title="GROUP_2:th.68">GROUP_2:68</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:58_1_1"/>
 <a href="group_9.html#K13" title="GROUP_9:func.13">Ker</a> <font color="Maroon" title="c4">g</font> is <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>
 <b>by </b><i><a class="ref" href="group_9.html#D10" target="_self" title="GROUP_9:def.10">Def10</a></i>;<br/>


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