Variety V[1040]

The variety generated by [6, 1040]: all semigroups that satisfy every identity of [6, 1040]. 4 semigroups of order six generate it, and 977 semigroups of order six lie in it.

Shortest known basis

3 identities irredundant

x² ≈ x³
x²yx ≈ yxy
xy²zt ≈ xyzt

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

7 identities, certified in Lean for 4 semigroups

Among the 505 varieties

Directly above: V[1110] V[2675] V[2771] V[2979] V[3258] V[3471] V[8219]
Directly below: V[976] V[993]

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[1040] in the inclusion graph, with everything above and below it.

Generated by 4 semigroups of order six

[6, 1040] [6, 1042] [6, 1098] [6, 1099]

Contains 977 semigroups of order six

The semigroups of order six that satisfy the basis.

Show all 977