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ApCoCoA-1:Mathieu11 group - Revision history
2024-03-28T17:54:14Z
Revision history for this page on the wiki
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http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:Mathieu11_group&diff=14011&oldid=prev
StrohmeierB: /* Mathieu group M {11} */
2014-04-22T21:00:33Z
<p><span dir="auto"><span class="autocomment">Mathieu group M {11}</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:00, 22 April 2014</td>
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<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>=== <div id="Mathieu11_group">[[:ApCoCoA:Symbolic data#Mathieu11_group|Mathieu <del class="diffchange diffchange-inline">group </del>M {11}]]</div> ===</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>=== <div id="Mathieu11_group">[[:ApCoCoA:Symbolic data#Mathieu11_group|Mathieu <ins class="diffchange diffchange-inline">Group </ins>M {11}]]</div> ===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== Description ====</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== Description ====</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The Mathieu group M11 is a sporadic group with order 7920 and it is a subgroup of the monstergroup.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The Mathieu group M11 is a sporadic group with order 7920 and it is a subgroup of the monstergroup.</div></td></tr>
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StrohmeierB
http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:Mathieu11_group&diff=13919&oldid=prev
StrohmeierB: /* Description */
2014-03-26T14:10:43Z
<p><span dir="auto"><span class="autocomment">Description</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:10, 26 March 2014</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== <div id="Mathieu11_group">[[:ApCoCoA:Symbolic data#Mathieu11_group|Mathieu group M {11}]]</div> ===</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== <div id="Mathieu11_group">[[:ApCoCoA:Symbolic data#Mathieu11_group|Mathieu group M {11}]]</div> ===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== Description ====</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== Description ====</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The Mathieu group M11 is a sporadic group with order 7920 and it is a subgroup of the monstergroup.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== Reference ====</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== Reference ====</div></td></tr>
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StrohmeierB
http://apcocoa.uni-passau.de/wiki/index.php?title=ApCoCoA-1:Mathieu11_group&diff=13918&oldid=prev
StrohmeierB: New page: === <div id="Mathieu11_group">Mathieu group M {11}</div> === ==== Description ==== ==== Reference ==== [http://brauer.maths.qmul.ac.uk/Atlas/v3/...
2014-03-26T14:03:21Z
<p>New page: === <div id="Mathieu11_group"><a href="/wiki/index.php?title=ApCoCoA-1:Symbolic_data#Mathieu11_group" class="mw-redirect" title="ApCoCoA-1:Symbolic data">Mathieu group M {11}</a></div> === ==== Description ==== ==== Reference ==== [http://brauer.maths.qmul.ac.uk/Atlas/v3/...</p>
<p><b>New page</b></p><div>=== <div id="Mathieu11_group">[[:ApCoCoA:Symbolic data#Mathieu11_group|Mathieu group M {11}]]</div> ===<br />
==== Description ====<br />
<br />
==== Reference ====<br />
[http://brauer.maths.qmul.ac.uk/Atlas/v3/group/M11/ ATLAS of Finite Group Representations - Version 3]<br />
==== Computation ====<br />
/*Use the ApCoCoA package ncpoly.*/<br />
<br />
Use ZZ/(2)[a,b];<br />
NC.SetOrdering("LLEX");<br />
<br />
Define CreateRelationsMathieuM11()<br />
Relations:=[];<br />
<br />
// add the relation a^2 = 1<br />
Append(Relations,[[a,a],[1]]);<br />
// add the relation b^4 = 1<br />
Append(Relations,[[b,b,b,b],[1]]);<br />
<br />
//add the relation (ab)^11 = 1<br />
Append(Relations, [[a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b],[1]]);<br />
<br />
//add the relation (ab^2)^6 = 1<br />
Append(Relations,[[a,b,b,a,b,b,a,b,b,a,b,b,a,b,b,a,b,b],[1]]);<br />
<br />
//add the relation ababab^{-1}abab^2ab^{-1}abab^{-1}ab^{-1} = 1<br />
Append(Relations,[[a,b,a,b,a,b,b,b,a,b,a,b,b,a,b,b,b,a,b,a,b,b,b,a,b,b,b],[1]]);<br />
<br />
Return Relations;<br />
EndDefine;<br />
<br />
Relations:=CreateRelationsMathieuM11();<br />
Relations;<br />
<br />
Gb:=NC.GB(Relations,31,1,100,1000);<br />
Gb;<br />
====Example in Symbolic Data Format====<br />
<FREEALGEBRA createdAt="2014-03-26" createdBy="strohmeier"><br />
<vars>a,b</vars><br />
<uptoDeg>27</uptoDeg><br />
<basis><br />
<ncpoly>a*a-1</ncpoly><br />
<ncpoly>b*b*b*b-1</ncpoly><br />
<ncpoly>(a*b)^11-1</ncpoly><br />
<ncpoly>(a*b*b)^6-1</ncpoly><br />
<ncpoly>a*b*a*b*a*b*b*b*a*b*a*b*b*a*b*b*b*a*b*a*b*b*b*a*b*b*b-1</ncpoly><br />
</basis><br />
<Comment>The partial LLex Gb has 15 elements</Comment><br />
<Comment>Mathieu group_M_{11}</Comment><br />
</FREEALGEBRA></div>
StrohmeierB