Variety V[3362]

The variety generated by [6, 3362]: all semigroups that satisfy every identity of [6, 3362]. 20 semigroups of order six generate it, and 913 semigroups of order six lie in it.

Shortest known basis

3 identities irredundant

x² ≈ x³
xyz ≈ xzy
x²yz ≈ xyz

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

5 identities, certified in Lean for 20 semigroups

Among the 505 varieties

Directly above: V[3303] V[3305] V[3367] V[3368] V[3810] V[5516] V[7541]
Directly below: V[988] V[1000] V[3178]

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[3362] in the inclusion graph, with everything above and below it.

Generated by 20 semigroups of order six

[6, 3362] [6, 3364] [6, 3379] [6, 3619] [6, 3621] [6, 3623] [6, 3972] [6, 3985] [6, 4002] [6, 4004] [6, 5894] [6, 5912] [6, 6155] [6, 6157] [6, 6160] [6, 6173] [6, 6178] [6, 6181] [6, 6625] [6, 9817]

Contains 913 semigroups of order six

The semigroups of order six that satisfy the basis.

Show all 913