Quellcode-Bibliothek gpolygons_blockdesign.include
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gap> LoadPackage("design");
-----------------------------------------------------------------------------
Loading DESIGN 1.6 (The Design Package for GAP)
by Leonard H. Soicher (http://www.maths.qmul.ac.uk/~leonard/).
Homepage: http://www.designtheory.org/software/gap_design/
-----------------------------------------------------------------------------
true
gap> gh := SplitCayleyHexagon(2);
H(2)
gap> CollineationGroup(gh);
#I for Split Cayley Hexagon
#I Computing nice monomorphism...
#I Found permutation domain...
G_2(2)
gap> des := BlockDesignOfGeneralisedPolygon(gh);
rec( autSubgroup := <permutation group with 3 generators>,
blocks := [ [ 1, 29, 52 ], [ 1, 34, 36 ], [ 1, 37, 48 ], [ 2, 13, 60 ],
[ 2, 44, 53 ], [ 2, 45, 52 ], [ 3, 17, 35 ], [ 3, 22, 51 ],
[ 3, 23, 48 ], [ 4, 16, 57 ], [ 4, 19, 36 ], [ 4, 54, 56 ],
[ 5, 22, 63 ], [ 5, 31, 57 ], [ 5, 49, 52 ], [ 6, 7, 60 ],
[ 6, 28, 57 ], [ 6, 35, 43 ], [ 7, 26, 27 ], [ 7, 33, 34 ],
[ 8, 9, 53 ], [ 8, 22, 33 ], [ 8, 38, 56 ], [ 9, 25, 61 ],
[ 9, 28, 37 ], [ 10, 18, 53 ], [ 10, 32, 35 ], [ 10, 36, 62 ],
[ 11, 12, 63 ], [ 11, 26, 54 ], [ 11, 37, 42 ], [ 12, 41, 43 ],
[ 12, 44, 50 ], [ 13, 15, 42 ], [ 13, 19, 51 ], [ 14, 15, 31 ],
[ 14, 17, 61 ], [ 14, 34, 50 ], [ 15, 20, 38 ], [ 16, 23, 44 ],
[ 16, 40, 59 ], [ 17, 45, 54 ], [ 18, 24, 26 ], [ 18, 30, 31 ],
[ 19, 25, 41 ], [ 20, 21, 62 ], [ 20, 23, 27 ], [ 21, 28, 55 ],
[ 21, 39, 45 ], [ 24, 29, 59 ], [ 24, 51, 55 ], [ 25, 27, 49 ],
[ 29, 38, 43 ], [ 30, 39, 41 ], [ 30, 46, 48 ], [ 32, 40, 42 ],
[ 32, 47, 49 ], [ 33, 39, 40 ], [ 46, 47, 56 ], [ 46, 58, 60 ],
[ 47, 50, 55 ], [ 58, 59, 61 ], [ 58, 62, 63 ] ], isBlockDesign := true,
v := 63 )
gap> f := GF(3);
GF(3)
gap> id := IdentityMat(2, f);;
gap> clan := List( f, t -> t*id );;
gap> clan := qClan(clan,f);
<q-clan over GF(3)>
gap> egq := EGQByqClan( clan );
#I Computed Kantor family. Now computing EGQ...
<EGQ of order [ 9, 3 ] and basepoint 0>
gap> HasElationGroup( egq );
true
gap> design := BlockDesignOfGeneralisedPolygon( egq );;
#I Computing orbits on lines of gen. polygon...
#I Computing block design of generalised polygon...
gap> aut := AutGroupBlockDesign( design );
<permutation group with 6 generators>
gap> NrBlockDesignPoints( design );
280
gap> NrBlockDesignBlocks( design );
112
gap> DisplayCompositionSeries(aut);
G (6 gens, size 26127360)
| Z(2)
S (5 gens, size 13063680)
| Z(2)
S (5 gens, size 6531840)
| Z(2)
S (4 gens, size 3265920)
| 2A(3,3) = U(4,3) ~ 2D(3,3) = O-(6,3)
1 (0 gens, size 1)
[ 0.83Quellennavigators
]
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2026-03-28
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