Quelle examples_PSL211.include Sprache: unbekannt

gap> g := PSL(2,11);
Group([ (3,11,9,7,5)(4,12,10,8,6), (1,2,8)(3,7,9)(4,10,5)(6,12,11) ])
gap> g1 := Group([ (1,2,3)(4,8,12)(5,10,9)(6,11,7), (1,2)(3,4)(5,12)(6,11)(7,10)(8,9) ]);
Group([ (1,2,3)(4,8,12)(5,10,9)(6,11,7), (1,2)(3,4)(5,12)(6,11)(7,10)(8,9) ])
gap> g2 := Group([ (1,2,7)(3,9,4)(5,11,10)(6,8,12), (1,2)(3,4)(5,12)(6,11)(7,10)(8,9) ]);
Group([ (1,2,7)(3,9,4)(5,11,10)(6,8,12), (1,2)(3,4)(5,12)(6,11)(7,10)(8,9) ])
gap> g3 := Group([ (1,2,11)(3,8,7)(4,9,5)(6,10,12), (1,2)(3,12)(4,11)(5,10)(6,9)(7,8) ]);
Group([ (1,2,11)(3,8,7)(4,9,5)(6,10,12), (1,2)(3,12)(4,11)(5,10)(6,9)(7,8) ])
gap> g4 := Group([ (1,2,11)(3,8,7)(4,9,5)(6,10,12), (1,2)(3,10)(4,9)(5,8)(6,7)(11,12) ]);
Group([ (1,2,11)(3,8,7)(4,9,5)(6,10,12), (1,2)(3,10)(4,9)(5,8)(6,7)(11,12) ])
gap> cg := CosetGeometry(g, [g1,g2,g3,g4]);
CosetGeometry( Group( [ ( 3,11, 9, 7, 5)( 4,12,10, 8, 6),
  ( 1, 2, 8)( 3, 7, 9)( 4,10, 5)( 6,12,11) ] ) )
gap> SetName(cg, "Gamma");
gap> ParabolicSubgroups(cg);
[ Group([ (1,2,3)(4,8,12)(5,10,9)(6,11,7), (1,2)(3,4)(5,12)(6,11)(7,10)
  (8,9) ]), Group([ (1,2,7)(3,9,4)(5,11,10)(6,8,12), (1,2)(3,4)(5,12)(6,11)
  (7,10)(8,9) ]), Group([ (1,2,11)(3,8,7)(4,9,5)(6,10,12), (1,2)(3,12)(4,11)
  (5,10)(6,9)(7,8) ]), Group([ (1,2,11)(3,8,7)(4,9,5)(6,10,12), (1,2)(3,10)
  (4,9)(5,8)(6,7)(11,12) ]) ]
gap> BorelSubgroup(cg);
Group(())
gap> AmbientGroup(cg);
Group([ (3,11,9,7,5)(4,12,10,8,6), (1,2,8)(3,7,9)(4,10,5)(6,12,11) ])
gap> type2 := ElementsOfIncidenceStructure( cg, 2 );
<elements of type 2 of Gamma>
gap> IsFlagTransitiveGeometry( cg );
true
gap> DrawDiagram( DiagramOfGeometry(cg), "PSL211");

Quelle examples_PSL211.include Sprache: unbekannt

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