A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 143 semigroups of order six, all of which generate the variety V[238]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-d128f8ca87b9cda3 in the data of the bases-min seal.
Certified for
[6, 238] [6, 245] [6, 255] [6, 330] [6, 335] [6, 400] [6, 415] [6, 424] [6, 436] [6, 498] [6, 504] [6, 549] [6, 556] [6, 562] [6, 570] [6, 576] [6, 579] [6, 582] [6, 636] [6, 646] [6, 649] [6, 676] [6, 726] [6, 732] [6, 737] [6, 743] [6, 821] [6, 823] [6, 838] [6, 842] [6, 847] [6, 850] [6, 1403] [6, 1414] [6, 1424] [6, 1463] [6, 1473] [6, 1481] [6, 1580] [6, 1583] [6, 1585] [6, 1635] [6, 1645] [6, 1654] [6, 1674] [6, 1677] [6, 1679] [6, 1698] [6, 1701] [6, 1703] [6, 1828] [6, 1830] [6, 1851] [6, 1855] [6, 1869] [6, 1871] [6, 2027] [6, 2029] [6, 2054] [6, 2060] [6, 2078] [6, 2084] [6, 2140] [6, 2146] [6, 2161] [6, 2163] [6, 2184] [6, 2188] [6, 2201] [6, 2203] [6, 2219] [6, 2221] [6, 2305] [6, 2314] [6, 2329] [6, 2351] [6, 2357] [6, 2362] [6, 2418] [6, 2421] [6, 2423] [6, 2465] [6, 2471] [6, 2476] [6, 2495] [6, 2497] [6, 2505] [6, 2507] [6, 4338] [6, 4347] [6, 4359] [6, 4399] [6, 4405] [6, 4466] [6, 4476] [6, 4482] [6, 4497] [6, 4501] [6, 4518] [6, 4521] [6, 4563] [6, 4595] [6, 4598] [6, 4625] [6, 4718] [6, 4722] [6, 4728] [6, 4730] [6, 4739] [6, 4741] [6, 4818] [6, 4821] [6, 4826] [6, 4830] [6, 4866] [6, 4872] [6, 4880] [6, 4934] [6, 4937] [6, 4970] [6, 4983] [6, 4989] [6, 4997] [6, 5027] [6, 5030] [6, 5048] [6, 5055] [6, 5061] [6, 5069] [6, 5075] [6, 5078] [6, 5081] [6, 9121] [6, 9125] [6, 9142] [6, 9174] [6, 9198] [6, 9208] [6, 9211] [6, 9224] [6, 9255] [6, 9257] [6, 9264]
The identities
- xy ≈ yx
- x³ ≈ x²y
- x³ ≈ xyz