Variety V[6432]
The variety generated by [6, 6432]: all semigroups that satisfy every identity of [6, 6432]. 2 semigroups of order six generate it, and 2,283 semigroups of order six lie in it.
Shortest known basis
8 identities reduced
- x² ≈ x³
- x²yx ≈ xyx
- xyxz² ≈ zxyxz
- xyzxz ≈ xyz²x
- x²yzy² ≈ x²zy²
- xyxztz ≈ xzyxtz
- xyzxtz ≈ zyx²tz
- xyztxz ≈ zyxtxz
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
- 16 identities, certified in Lean for 2 semigroups
Among the 505 varieties
- Directly above
- none: a maximal variety of the census
- 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[6432] in the inclusion graph, with everything above and below it.
Generated by 2 semigroups of order six
Contains 2,283 semigroups of order six
The semigroups of order six that satisfy the basis.