Quelle aboutCoxeter.html Sprache: HTML

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            <td style="vertical-align: top;"><a
href="aboutArtinGroups.html"><small style="color: rgb(0, 0, 102);">Previous</small></a><br>
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            <td
style="text-align: center; vertical-align: top; color: rgb(0, 0, 102);"><big><span
style="font-weight: bold;">About HAP: Resolutions for Coxeter groups<br>
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            <td style="text-align: right; vertical-align: top;"><a
href="aboutCohomologyRings.html"><small style="color: rgb(0, 0, 102);">next</small></a><br>
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style="vertical-align: top; background-color: rgb(255, 255, 255); text-align: left;">A
Coxeter group is a finitely presented group obtained from an Artin
presentation by imposing the extra relations x<sup>2</sup>=1 on all
Artin generators x. The resolution for certain (and conjecturally all)
Artin groups described on the preceding page leads to a resolution for
all Coxeter groups. At present this resolution has only been
implemented in HAP for finite Coxeter groups and only in dimensions
less than or equal to n where n denotes the number of generators in the
Coxeter presentation.<br>
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      <td
style="vertical-align: top; background-color: rgb(255, 255, 255);">The
following commands compute 7 terms of a free resolution for the
symmetric group on 8 letters, and then use this resolution to construct
a resolution for its alternating subgroup of index 2.<br>
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style="background-color: rgb(255, 255, 204); vertical-align: top;">gap>
D:=[[1,[2,3]],[2,[3,3]],[3,[4,3]],[4,[5,3]],[5,[6,3]],[6,[7,3]]];;<br>
gap> R:=ResolutionCoxeterGroup(D,7);;<br>
gap> S:=ResolutionFiniteSubgroup(R,AlternatingGroup(8));;<br>
gap> Homology(TensorWithIntegers(S),4);<br>
[ 2 ]<br>
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href="aboutContents.html"><span style="color: rgb(0, 0, 102);">Contents</span></a><br>
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href="aboutCohomologyRings.html"><span style="color: rgb(0, 0, 102);">Next
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