http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:Other13%22_groups&feed=atom&action=historyApCoCoA-1:Other13" groups - Revision history2024-03-28T21:55:14ZRevision history for this page on the wikiMediaWiki 1.35.0http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:Other13%22_groups&diff=13813&oldid=prevF lorenz: New page: === <div id="Other13_groups">Other groups</div> === ==== Description ==== This group has the following finite representation: G = <x,y | x^2 = xy^{...2013-09-18T15:59:00Z<p>New page: === <div id="Other13_groups"><a href="/wiki/index.php?title=ApCoCoA-1:Symbolic_data#Other_groups" class="mw-redirect" title="ApCoCoA-1:Symbolic data">Other groups</a></div> === ==== Description ==== This group has the following finite representation: G = <x,y | x^2 = xy^{...</p>
<p><b>New page</b></p><div>=== <div id="Other13_groups">[[:ApCoCoA:Symbolic data#Other_groups|Other groups]]</div> ===<br />
==== Description ====<br />
This group has the following finite representation:<br />
G = <x,y | x^2 = xy^{a}xy^{b}xy^{c}xy^{d} = 1><br />
<br />
==== Reference ==== <br />
No reference available<br />
<br />
==== Computation ====<br />
<br />
/*Use the ApCoCoA package ncpoly.*/<br />
<br />
// Note that a,b >= 1 and n >= 2<br />
MEMORY.A := 3;<br />
MEMORY.B := 3;<br />
MEMORY.C := 4;<br />
MEMORY.D := 5;<br />
// y is invers to z, the invers element of x follows directly from the relation x^2 = 1<br />
Use ZZ/(2)[x,y,z];<br />
NC.SetOrdering("LLEX");<br />
Define CreateRelationsOther13()<br />
Relations:=[];<br />
<br />
// add the relation of the invers elements yz = zy = 1<br />
Append(Relations,[[y,z],[1]]);<br />
Append(Relations,[[z,y],[1]]);<br />
<br />
// add the relation x^2 = 1<br />
Append(Relations,[[x,x],[1]]);<br />
<br />
// add the relation xy^{a}xy^{b}xy^{c}xy^{d}<br />
Append(Relations,[[x,y^(MEMORY.A),x,y^(MEMORY.B),x,y^(MEMORY.C),x,y^(MEMORY.D)],[1]]);<br />
Return Relations;<br />
EndDefine;<br />
<br />
Relations:=CreateRelationsOther13();<br />
GB:=NC.GB(Relations,31,1,100,1000);</div>F lorenz