Variety V[5614]
The variety generated by [6, 5614]: all semigroups that satisfy every identity of [6, 5614]. 4 semigroups of order six generate it, and 9,170 semigroups of order six lie in it.
Shortest known basis
7 identities reduced
- x³ ≈ x⁴
- xyxy ≈ xy²x
- x³yx ≈ x²yx
- x²yz ≈ xyxz
- xyzxy ≈ xyzyx
- xyzxz ≈ xyz²x
- xyztxz ≈ xyztzx
Reduced as far as the search went: some identity may still follow from the others. Obtained from a certified basis by removing identities that follow from the others (Vampire). Shortest known, not known to be minimal.
Certified bases
- 7 identities, certified in Lean for 4 semigroups
Among the 505 varieties
- Directly above
- Directly below
A variety lies above another when it contains it. An inclusion holds when the basis of the smaller variety derives that of the larger one, proved by Vampire; it fails when a semigroup of order six lies in the one and not in the other.
Explore V[5614] in the inclusion graph, with everything above and below it.
Generated by 4 semigroups of order six
Contains 9,170 semigroups of order six
The semigroups of order six that satisfy the basis.