Quelle diagram_neumaier.include
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Untersuchungsergebnis.include Download desUnknown {[0] [0] [0]}zum Wurzelverzeichnis wechseln
Alt( [ 1 .. 8 ] )
gap> pabs:= [
> Group([ (2,4,6), (1,3,2)(4,8)(6,7) ]),
> Group([ (1,6,7,8,4), (2,5)(3,4) ]),
> Group([ (3,6)(7,8), (2,4,5), (1,5)(2,4), (2,4)(6,7), (6,8,7),
> (1,2)(4,5), (3,7)(6,8) ]),
> Group([ (1,7,8,4)(2,5,3,6), (1,3)(2,6)(4,8)(5,7), (1,5)(2,4)(3,7)(6,8),
> (1,8)(2,7)(3,4)(5,6), (1,3)(2,6)(4,7)(5,8) ]) ];
[ Group([ (2,4,6), (1,3,2)(4,8)(6,7) ]), Group([ (1,6,7,8,4), (2,5)(3,4) ]),
Group([ (3,6)(7,8), (2,4,5), (1,5)(2,4), (2,4)(6,7), (6,8,7), (1,2)
(4,5), (3,7)(6,8) ]), Group([ (1,7,8,4)(2,5,3,6), (1,3)(2,6)(4,8)
(5,7), (1,5)(2,4)(3,7)(6,8), (1,8)(2,7)(3,4)(5,6), (1,3)(2,6)(4,7)(5,8) ]) ]
gap> cg:=CosetGeometry(g,pabs);
CosetGeometry( AlternatingGroup( [ 1 .. 8 ] ) )
gap> diag:=DiagramOfGeometry(cg);
< Diagram of CosetGeometry( AlternatingGroup( [ 1 .. 8 ] ) ,
[ Group( [ (2,4,6), (1,3,2)(4,8)(6,7) ] ),
Group( [ (1,6,7,8,4), (2,5)(3,4) ] ),
Group( [ (3,6)(7,8), (2,4,5), (1,5)(2,4), (2,4)(6,7), (6,8,7), (1,2)(4,5),
(3,7)(6,8) ] ),
Group( [ (1,7,8,4)(2,5,3,6), (1,3)(2,6)(4,8)(5,7), (1,5)(2,4)(3,7)(6,8),
(1,8)(2,7)(3,4)(5,6), (1,3)(2,6)(4,7)(5,8) ] ) ] ) >
gap> DrawDiagram(diag, "neuma8");
gap> #Exec("gv neuma8.ps");
gap> point:=Random(ElementsOfIncidenceStructure(cg,1));
<element of type 1 of CosetGeometry( AlternatingGroup( [ 1 .. 8 ] ) )>
gap> residue:=ResidueOfFlag(FlagOfIncidenceStructure(cg,[point]));
CosetGeometry( Group( [ (3,5,7), (1,7)(2,4,3)(5,8) ] ) )
gap> diagc3:=DiagramOfGeometry(residue);
< Diagram of CosetGeometry( Group( [ (3,5,7), (1,7)(2,4,3)(5,8) ] ) ,
[ Group( [ (4,5,8), (1,4,5), (1,7,8), (1,8,4,2,7) ] ),
Group( [ (1,8)(4,7), (2,5,3), (1,7)(2,3), (1,7,8), (1,4)(7,8) ] ),
Group( [ (1,5,4,3)(7,8), (2,4)(5,8) ] ) ] ) >
gap> DrawDiagram(diagc3, "a7geo");
gap> #Exec("gv a7geo.ps");
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2026-03-28
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