Variety V[3810]

The variety generated by [6, 3810]: all semigroups that satisfy every identity of [6, 3810]. 8 semigroups of order six generate it, and 1,197 semigroups of order six lie in it.

Shortest known basis

4 identities irredundant

x² ≈ x³
x²y ≈ xyx
xyz ≈ xyz²
xy²z ≈ xzyz

Irredundant: none of these identities follows from the others; for each, a semigroup satisfies the others but not it. 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 8 semigroups

Among the 505 varieties

Directly above: V[3811] V[3812] V[3930] V[5635] V[6510] V[7390] V[7624]
Directly below: V[3059] V[3301] V[3362]

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[3810] in the inclusion graph, with everything above and below it.

Generated by 8 semigroups of order six

[6, 3810] [6, 3816] [6, 3823] [6, 3829] [6, 6433] [6, 6438] [6, 6440] [6, 6445]

Contains 1,197 semigroups of order six

The semigroups of order six that satisfy the basis.

Show all 1,197