Residuated Chains

Subdirectly Irreducible Nil Semigroups of order 6

list:=[
[# 1
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[ 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
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[# 2
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[# 3
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[ 0, 0, 1, 0, 0, 2 ]
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[# 4
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[ 0, 0, 1, 0, 1, 0 ]
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[# 5
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[# 6
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[ 0, 0, 1, 0, 1, 2 ]
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[# 7
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[ 0, 0, 1, 0, 2, 3 ]
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[# 8
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[# 9
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[# 10
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[ 0, 0, 1, 0, 1, 1 ]
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[# 11
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[ 0, 0, 1, 0, 1, 2 ]
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[# 12
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[ 0, 0, 1, 0, 2, 3 ]
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[# 13
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[ 0, 0, 1, 0, 3, 2 ]
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[# 14
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[ 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 3, 0 ],
[ 0, 0, 1, 0, 0, 2 ]
],
[# 15
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[ 0, 0, 0, 1, 3, 1 ],
[ 0, 0, 1, 0, 1, 2 ]
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[# 16
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[ 0, 0, 1, 1, 1, 0 ]
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[# 17
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[ 0, 0, 1, 1, 1, 1 ]
],
[# 18
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[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 2 ]
],
[# 19
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[ 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 0, 2 ],
[ 0, 0, 1, 1, 2, 3 ]
],
[# 20
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[ 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
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[ 0, 0, 1, 1, 0, 0 ]
],
[# 21
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[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 1, 0 ],
[ 0, 0, 1, 1, 0, 1 ]
],
[# 22
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[ 0, 0, 0, 0, 1, 1 ],
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[ 0, 0, 1, 1, 0, 2 ]
],
[# 23
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[ 0, 0, 0, 0, 0, 1 ],
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[ 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 1, 0 ]
],
[# 24
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[ 0, 0, 1, 1, 1, 1 ]
],
[# 25
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[ 0, 0, 1, 1, 1, 2 ]
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[# 26
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[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 1, 2 ],
[ 0, 0, 1, 1, 2, 3 ]
],
[# 27
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[ 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 2, 3 ],
[ 0, 0, 1, 1, 3, 3 ]
],
[# 28
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[ 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 1, 3, 3 ],
[ 0, 0, 1, 1, 3, 3 ]
],
[# 29
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[ 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 2 ],
[ 0, 0, 0, 1, 1, 2 ],
[ 0, 0, 1, 2, 2, 4 ]
],
[# 30
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[ 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 2 ],
[ 0, 0, 0, 1, 2, 3 ],
[ 0, 0, 1, 2, 3, 4 ]
],
[# 31
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[ 0, 0, 0, 0, 0, 1 ],
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[ 0, 0, 1, 0, 0, 0 ]
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[# 32
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[# 33
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[# 34
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[# 35
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[# 36
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[# 37
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[# 38
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[# 39
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[# 40
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[# 41
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[# 42
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[# 43
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[# 44
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[# 45
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[# 46
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[# 47
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[# 48
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[# 49
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[# 50
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[# 51
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[# 52
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[# 53
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[# 54
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[# 55
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[# 56
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[# 57
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[# 58
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[# 59
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[# 60
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[# 61
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[# 62
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[# 63
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[# 64
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[# 65
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[# 66
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[# 67
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[# 68
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[ 0, 0, 1, 1, 0, 1 ]
]
];
Computed by Peter Jipsen using GAP 3.4 (this list can be copied and read into GAP)