Variety V[3371]

The variety generated by [6, 3371]: all semigroups that satisfy every identity of [6, 3371]. 2 semigroups of order six generate it, and 941 semigroups of order six lie in it.

Shortest known basis

4 identities irredundant

x² ≈ x³
xyx ≈ yx²
x²yz ≈ xyz
xyxz ≈ xy²z

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 2 semigroups

Among the 505 varieties

Directly above: V[3372] V[3942] V[5580] V[6169] V[7428] V[7438] V[13184]
Directly below: V[993] V[3197] V[5919]

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[3371] in the inclusion graph, with everything above and below it.

Generated by 2 semigroups of order six

[6, 3371] [6, 3377]

Contains 941 semigroups of order six

The semigroups of order six that satisfy the basis.

Show all 941