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# Some small pregroups
# The lists of small pregroups were generated by
# Chris Jefferson <caj21@st-andrews.ac.uk> and
# Richard Parker.
ANATPH_small_pregroups[1] :=
[ [ [ 1 ] ] ];
ANATPH_small_pregroups[2] :=
[ [ [1, 2],
[2, 1] ] ];
ANATPH_small_pregroups[3] :=
[ [ [1, 2, 3],
[2, 1, 0],
[3, 0, 1] ] ];
# missing: Cyclic group of order 3
ANATPH_small_pregroups[4] :=
[ [ [1, 2, 3, 4],
[2, 1, 0, 0],
[3, 0, 1, 0],
[4, 0, 0, 1] ],
[ [1, 2, 3, 4],
[2, 1, 4, 3],
[3, 4, 1, 2],
[4, 3, 2, 1] ],
[ [1, 2, 3, 4],
[2, 1, 0, 0],
[3, 0, 0, 1],
[4, 0, 1, 0] ],
[ [1, 2, 3, 4],
[2, 1, 0, 0],
[3, 0, 4, 1],
[4, 0, 1, 3] ],
[ [1, 2, 3, 4],
[2, 1, 4, 3],
[3, 4, 2, 1],
[4, 3, 1, 2] ] ];
ANATPH_small_pregroups[5] :=
[ [ [1, 2, 3, 4, 5],
[2, 1, 0, 0, 0],
[3, 0, 1, 0, 0],
[4, 0, 0, 1, 0],
[5, 0, 0, 0, 1] ],
[ [1, 2, 3, 4, 5],
[2, 1, 4, 3, 0],
[3, 4, 1, 2, 0],
[4, 3, 2, 1, 0],
[5, 0, 0, 0, 1]],
[ [1, 2, 3, 4, 5],
[2, 1, 0, 0, 0],
[3, 0, 1, 0, 0],
[4, 0, 0, 0, 1],
[5, 0, 0, 1, 0]],
[ [1, 2, 3, 4, 5],
[2, 1, 0, 0, 0],
[3, 0, 1, 0, 0],
[4, 0, 0, 5, 1],
[5, 0, 0, 1, 4]],
[ [1, 2, 3, 4, 5],
[2, 1, 4, 3, 0],
[3, 4, 2, 1, 0],
[4, 3, 1, 2, 0],
[5, 0, 0, 0, 1]],
[ [1, 2, 3, 4, 5],
[2, 0, 1, 0, 0],
[3, 1, 0, 0, 0],
[4, 0, 0, 0, 1],
[5, 0, 0, 1, 0]],
[ [1, 2, 3, 4, 5],
[2, 3, 1, 0, 0],
[3, 1, 2, 0, 0],
[4, 0, 0, 0, 1],
[5, 0, 0, 1, 0]],
[ [1, 2, 3, 4, 5],
[2, 3, 1, 0, 0],
[3, 1, 2, 0, 0],
[4, 0, 0, 5, 1],
[5, 0, 0, 1, 4]],
[ [1, 2, 3, 4, 5],
[2, 3, 4, 5, 1],
[3, 4, 5, 1, 2],
[4, 5, 1, 2, 3],
[5, 1, 2, 3, 4]]];
ANATPH_small_pregroups[6] :=
[ [ [1,2,3,4,5,6],
[2,1,0,5,4,0],
[3,6,0,1,0,0],
[4,0,1,0,0,2],
[5,0,2,0,0,1],
[6,3,0,0,1,0] ],
[ [1,2,3,4,5,6],
[2,1,5,0,3,0],
[3,0,0,1,0,2],
[4,6,1,0,0,0],
[5,0,0,2,0,1],
[6,4,0,0,1,0] ],
[ [1,2,3,4,5,6],
[2,1,0,6,0,4],
[3,5,0,1,0,0],
[4,0,1,0,2,0],
[5,3,0,0,0,1],
[6,0,2,0,1,0] ],
[ [1,2,3,4,5,6],
[2,1,5,6,3,4],
[3,5,0,1,0,2],
[4,6,1,0,2,0],
[5,3,0,2,0,1],
[6,4,2,0,1,0] ],
[ [1,2,3,4,5,6],
[2,1,6,0,0,3],
[3,0,0,1,2,0],
[4,5,1,0,0,0],
[5,4,0,0,0,1],
[6,0,0,2,1,0] ],
[ [1,2,3,4,5,6],
[2,1,6,5,4,3],
[3,6,0,1,2,0],
[4,5,1,0,0,2],
[5,4,2,0,0,1],
[6,3,0,2,1,0] ],
[ [1,2,3,4,5,6],
[2,1,5,6,3,4],
[3,6,1,0,0,2],
[4,5,0,1,2,0],
[5,4,2,0,0,1],
[6,3,0,2,1,0] ],
[ [1,2,3,4,5,6],
[2,1,0,6,0,4],
[3,0,1,5,4,0],
[4,5,6,1,2,3],
[5,4,0,3,0,1],
[6,0,4,2,1,0] ],
[ [1,2,3,4,5,6],
[2,1,0,5,4,0],
[3,0,1,6,0,4],
[4,6,5,1,3,2],
[5,0,4,2,0,1],
[6,4,0,3,1,0] ],
[ [1,2,3,4,5,6],
[2,1,6,0,0,3],
[3,5,1,6,2,4],
[4,0,5,1,3,0],
[5,3,4,0,0,1],
[6,0,2,3,1,0] ],
[ [1,2,3,4,5,6],
[2,1,4,3,6,5],
[3,4,1,2,0,0],
[4,3,2,1,0,0],
[5,6,0,0,2,1],
[6,5,0,0,1,2] ],
[ [1,2,3,4,5,6],
[2,1,4,3,0,0],
[3,4,1,2,6,5],
[4,3,2,1,0,0],
[5,0,6,0,3,1],
[6,0,5,0,1,3] ],
[ [1,2,3,4,5,6],
[2,1,4,3,0,0],
[3,4,1,2,0,0],
[4,3,2,1,6,5],
[5,0,0,6,4,1],
[6,0,0,5,1,4] ],
[ [1,2,3,4,5,6],
[2,1,6,5,4,3],
[3,6,1,0,0,2],
[4,5,0,1,2,0],
[5,4,0,2,1,0],
[6,3,2,0,0,1] ],
[ [1,2,3,4,5,6],
[2,1,6,0,0,3],
[3,6,1,5,4,2],
[4,0,5,1,3,0],
[5,0,4,3,1,0],
[6,3,2,0,0,1] ],
[ [1,2,3,4,5,6],
[2,1,5,6,3,4],
[3,5,1,0,2,0],
[4,6,0,1,0,2],
[5,3,2,0,1,0],
[6,4,0,2,0,1] ],
[ [1,2,3,4,5,6],
[2,1,0,6,0,4],
[3,0,1,5,4,0],
[4,6,5,1,3,2],
[5,0,4,3,1,0],
[6,4,0,2,0,1] ],
[ [1,2,3,4,5,6],
[2,1,5,0,3,0],
[3,5,1,6,2,4],
[4,0,6,1,0,3],
[5,3,2,0,1,0],
[6,0,4,3,0,1] ],
[ [1,2,3,4,5,6],
[2,1,0,5,4,0],
[3,0,1,6,0,4],
[4,5,6,1,2,3],
[5,4,0,2,1,0],
[6,0,4,3,0,1] ],
[ [1,2,3,4,5,6],
[2,1,4,3,6,5],
[3,4,1,2,0,0],
[4,3,2,1,0,0],
[5,6,0,0,1,2],
[6,5,0,0,2,1] ],
[ [1,2,3,4,5,6],
[2,1,0,0,6,5],
[3,0,1,5,4,0],
[4,0,5,1,3,0],
[5,6,4,3,1,2],
[6,5,0,0,2,1] ],
[ [1,2,3,4,5,6],
[2,1,0,0,6,5],
[3,0,1,6,0,4],
[4,0,6,1,0,3],
[5,6,0,0,1,2],
[6,5,4,3,2,1] ],
[ [1,2,3,4,5,6],
[2,1,4,3,0,0],
[3,4,1,2,6,5],
[4,3,2,1,0,0],
[5,0,6,0,1,3],
[6,0,5,0,3,1] ],
[ [1,2,3,4,5,6],
[2,1,0,5,4,0],
[3,0,1,0,6,5],
[4,5,0,1,2,0],
[5,4,6,2,1,3],
[6,0,5,0,3,1] ],
[ [1,2,3,4,5,6],
[2,1,0,6,0,4],
[3,0,1,0,6,5],
[4,6,0,1,0,2],
[5,0,6,0,1,3],
[6,4,5,2,3,1] ],
[ [1,2,3,4,5,6],
[2,1,4,3,0,0],
[3,4,1,2,0,0],
[4,3,2,1,6,5],
[5,0,0,6,1,4],
[6,0,0,5,4,1] ],
[ [1,2,3,4,5,6],
[2,1,5,0,3,0],
[3,5,1,0,2,0],
[4,0,0,1,6,5],
[5,3,2,6,1,4],
[6,0,0,5,4,1] ],
[ [1,2,3,4,5,6],
[2,1,6,0,0,3],
[3,6,1,0,0,2],
[4,0,0,1,6,5],
[5,0,0,6,1,4],
[6,3,2,5,4,1] ]
];
ANATPH_small_pregroups[7] :=
[ [ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 0, 0, 0, 0, 0],
[3, 0, 1, 0, 0, 0, 0],
[4, 0, 0, 1, 0, 0, 0],
[5, 0, 0, 0, 1, 0, 0],
[6, 0, 0, 0, 0, 1, 0],
[7, 0, 0, 0, 0, 0, 1] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 0, 0, 0],
[3, 4, 1, 2, 0, 0, 0],
[4, 3, 2, 1, 0, 0, 0],
[5, 0, 0, 0, 1, 0, 0],
[6, 0, 0, 0, 0, 1, 0],
[7, 0, 0, 0, 0, 0, 1] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 0, 0, 0],
[3, 4, 1, 2, 0, 0, 0],
[4, 3, 2, 1, 0, 0, 0],
[5, 0, 0, 0, 1, 7, 6],
[6, 0, 0, 0, 7, 1, 5],
[7, 0, 0, 0, 6, 5, 1] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 6, 5, 0],
[3, 4, 1, 2, 0, 0, 0],
[4, 3, 2, 1, 0, 0, 0],
[5, 6, 0, 0, 1, 2, 0],
[6, 5, 0, 0, 2, 1, 0],
[7, 0, 0, 0, 0, 0, 1] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 0, 0, 0, 0, 0],
[3, 0, 1, 0, 0, 0, 0],
[4, 0, 0, 1, 0, 0, 0],
[5, 0, 0, 0, 1, 0, 0],
[6, 0, 0, 0, 0, 0, 1],
[7, 0, 0, 0, 0, 1, 0] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 0, 0, 0, 0, 0],
[3, 0, 1, 0, 0, 0, 0],
[4, 0, 0, 1, 0, 0, 0],
[5, 0, 0, 0, 1, 0, 0],
[6, 0, 0, 0, 0, 7, 1],
[7, 0, 0, 0, 0, 1, 6] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 0, 0, 0],
[3, 4, 1, 2, 0, 0, 0],
[4, 3, 2, 1, 0, 0, 0],
[5, 0, 0, 0, 1, 0, 0],
[6, 0, 0, 0, 0, 0, 1],
[7, 0, 0, 0, 0, 1, 0] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 0, 0, 0],
[3, 4, 1, 2, 0, 0, 0],
[4, 3, 2, 1, 0, 0, 0],
[5, 0, 0, 0, 1, 0, 0],
[6, 0, 0, 0, 0, 7, 1],
[7, 0, 0, 0, 0, 1, 6] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 0, 0, 0],
[3, 4, 1, 2, 0, 0, 0],
[4, 3, 2, 1, 0, 0, 0],
[5, 0, 0, 0, 1, 7, 6],
[6, 0, 0, 0, 7, 5, 1],
[7, 0, 0, 0, 6, 1, 5] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 6, 5, 0],
[3, 4, 1, 2, 0, 0, 0],
[4, 3, 2, 1, 0, 0, 0],
[5, 6, 0, 0, 2, 1, 0],
[6, 5, 0, 0, 1, 2, 0],
[7, 0, 0, 0, 0, 0, 1] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 6, 5, 0],
[3, 5, 1, 0, 2, 0, 0],
[4, 6, 2, 0, 1, 0, 0],
[5, 3, 0, 1, 0, 2, 0],
[6, 4, 0, 2, 0, 1, 0],
[7, 0, 0, 0, 0, 0, 1] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 6, 5, 0],
[3, 5, 1, 6, 2, 4, 0],
[4, 6, 2, 5, 1, 3, 0],
[5, 3, 6, 1, 4, 2, 0],
[6, 4, 5, 2, 3, 1, 0],
[7, 0, 0, 0, 0, 0, 1] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 0, 0, 0, 0, 0],
[3, 0, 1, 0, 0, 0, 0],
[4, 0, 0, 0, 1, 0, 0],
[5, 0, 0, 1, 0, 0, 0],
[6, 0, 0, 0, 0, 0, 1],
[7, 0, 0, 0, 0, 1, 0] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 0, 0, 0, 0, 0],
[3, 0, 1, 0, 0, 0, 0],
[4, 0, 0, 5, 1, 0, 0],
[5, 0, 0, 1, 4, 0, 0],
[6, 0, 0, 0, 0, 0, 1],
[7, 0, 0, 0, 0, 1, 0] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 0, 0, 0, 0, 0],
[3, 0, 1, 0, 0, 0, 0],
[4, 0, 0, 5, 1, 0, 0],
[5, 0, 0, 1, 4, 0, 0],
[6, 0, 0, 0, 0, 7, 1],
[7, 0, 0, 0, 0, 1, 6] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 0, 0, 0, 0, 0],
[3, 0, 1, 0, 0, 0, 0],
[4, 0, 0, 5, 6, 7, 1],
[5, 0, 0, 6, 7, 1, 4],
[6, 0, 0, 7, 1, 4, 5],
[7, 0, 0, 1, 4, 5, 6] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 0, 0, 0],
[3, 4, 2, 1, 0, 0, 0],
[4, 3, 1, 2, 0, 0, 0],
[5, 0, 0, 0, 1, 0, 0],
[6, 0, 0, 0, 0, 1, 0],
[7, 0, 0, 0, 0, 0, 1] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 0, 0, 0],
[3, 4, 2, 1, 0, 0, 0],
[4, 3, 1, 2, 0, 0, 0],
[5, 0, 0, 0, 1, 0, 0],
[6, 0, 0, 0, 0, 0, 1],
[7, 0, 0, 0, 0, 1, 0] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 0, 0, 0],
[3, 4, 2, 1, 0, 0, 0],
[4, 3, 1, 2, 0, 0, 0],
[5, 0, 0, 0, 1, 0, 0],
[6, 0, 0, 0, 0, 7, 1],
[7, 0, 0, 0, 0, 1, 6] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 0, 0, 0],
[3, 4, 2, 1, 0, 0, 0],
[4, 3, 1, 2, 0, 0, 0],
[5, 0, 0, 0, 1, 7, 6],
[6, 0, 0, 0, 7, 5, 1],
[7, 0, 0, 0, 6, 1, 5] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 6, 5, 0],
[3, 4, 2, 1, 0, 0, 0],
[4, 3, 1, 2, 0, 0, 0],
[5, 6, 0, 0, 2, 1, 0],
[6, 5, 0, 0, 1, 2, 0],
[7, 0, 0, 0, 0, 0, 1] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 0, 0, 0],
[3, 0, 0, 0, 1, 2, 0],
[4, 0, 0, 0, 2, 1, 0],
[5, 6, 1, 0, 0, 0, 0],
[6, 5, 0, 1, 0, 0, 0],
[7, 0, 0, 0, 0, 0, 1] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 0, 0, 0],
[3, 0, 0, 0, 1, 2, 4],
[4, 0, 0, 0, 2, 1, 3],
[5, 6, 1, 7, 0, 0, 0],
[6, 5, 7, 1, 0, 0, 0],
[7, 0, 0, 0, 6, 5, 1] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 6, 5, 0],
[3, 4, 0, 0, 1, 2, 0],
[4, 3, 0, 0, 2, 1, 0],
[5, 6, 1, 2, 0, 0, 0],
[6, 5, 2, 1, 0, 0, 0],
[7, 0, 0, 0, 0, 0, 1] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 1, 4, 3, 6, 5, 0],
[3, 4, 5, 6, 1, 2, 0],
[4, 3, 6, 5, 2, 1, 0],
[5, 6, 1, 2, 3, 4, 0],
[6, 5, 2, 1, 4, 3, 0],
[7, 0, 0, 0, 0, 0, 1] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 0, 1, 0, 0, 0, 0],
[3, 1, 0, 0, 0, 0, 0],
[4, 0, 0, 0, 1, 0, 0],
[5, 0, 0, 1, 0, 0, 0],
[6, 0, 0, 0, 0, 0, 1],
[7, 0, 0, 0, 0, 1, 0] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 3, 1, 0, 0, 0, 0],
[3, 1, 2, 0, 0, 0, 0],
[4, 0, 0, 0, 1, 0, 0],
[5, 0, 0, 1, 0, 0, 0],
[6, 0, 0, 0, 0, 0, 1],
[7, 0, 0, 0, 0, 1, 0] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 3, 1, 0, 0, 0, 0],
[3, 1, 2, 0, 0, 0, 0],
[4, 0, 0, 5, 1, 0, 0],
[5, 0, 0, 1, 4, 0, 0],
[6, 0, 0, 0, 0, 0, 1],
[7, 0, 0, 0, 0, 1, 0] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 3, 1, 0, 0, 0, 0],
[3, 1, 2, 0, 0, 0, 0],
[4, 0, 0, 5, 1, 0, 0],
[5, 0, 0, 1, 4, 0, 0],
[6, 0, 0, 0, 0, 7, 1],
[7, 0, 0, 0, 0, 1, 6] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 0, 1, 5, 0, 0, 0],
[3, 1, 0, 0, 4, 0, 0],
[4, 0, 0, 0, 0, 1, 3],
[5, 0, 0, 0, 0, 2, 1],
[6, 0, 7, 1, 0, 0, 0],
[7, 6, 0, 0, 1, 0, 0] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 3, 1, 0, 0, 0, 0],
[3, 1, 2, 0, 0, 0, 0],
[4, 0, 0, 5, 6, 7, 1],
[5, 0, 0, 6, 7, 1, 4],
[6, 0, 0, 7, 1, 4, 5],
[7, 0, 0, 1, 4, 5, 6] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 3, 4, 5, 1, 0, 0],
[3, 4, 5, 1, 2, 0, 0],
[4, 5, 1, 2, 3, 0, 0],
[5, 1, 2, 3, 4, 0, 0],
[6, 0, 0, 0, 0, 0, 1],
[7, 0, 0, 0, 0, 1, 0] ],
[ [1, 2, 3, 4, 5, 6, 7],
[2, 3, 4, 5, 6, 7, 1],
[3, 4, 5, 6, 7, 1, 2],
[4, 5, 6, 7, 1, 2, 3],
[5, 6, 7, 1, 2, 3, 4],
[6, 7, 1, 2, 3, 4, 5],
[7, 1, 2, 3, 4, 5, 6] ]
];
InstallGlobalFunction("NrSmallPregroups",
function(n)
if not IsPosInt(n) then
Error("n has to be a positive integer");
fi;
if IsBound(ANATPH_small_pregroups[n]) then
return Length(ANATPH_small_pregroups[n]);
fi;
return fail;
end);
InstallGlobalFunction("SmallPregroup",
function(n,i)
local names;
if not IsPosInt(n) then
Error("n has to be a positive integer");
fi;
if IsPosInt(i) and
IsBound(ANATPH_small_pregroups[n]) and
IsBound(ANATPH_small_pregroups[n][i]) then
names := Concatenation( ["1"]
, List([2..n], y -> Concatenation("p", String(y-1))));
return PregroupByTable(names, ANATPH_small_pregroups[n][i]);
else
Error("small pregroup of size ", n, " with index ", i, " not available");
fi;
end);
[ Dauer der Verarbeitung: 0.33 Sekunden
(vorverarbeitet)
]
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