Variety V[2583]
The variety generated by [6, 2583]: all semigroups that satisfy every identity of [6, 2583]. 2 semigroups of order six generate it, and 305 semigroups of order six lie in it.
Shortest known basis
4 identities reduced
- xy ≈ yx
- x³y ≈ xy³
- x⁵ ≈ xy²z²
- xyztu ≈ xyztu³
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
- 6 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[2583] in the inclusion graph, with everything above and below it.
Generated by 2 semigroups of order six
Contains 305 semigroups of order six
The semigroups of order six that satisfy the basis.