Variety V[974]

The variety generated by [6, 974]: all semigroups that satisfy every identity of [6, 974]. 9 semigroups of order six generate it, and 11 semigroups of order six lie in it.

Shortest known basis

1 identity irredundant

x² ≈ xy

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

1 identity, certified in Lean for 9 semigroups

Among the 505 varieties

Directly above: V[1000] V[3095] V[3178] V[3318] V[8713]
Directly below: V[1] V[15854]

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

Generated by 9 semigroups of order six

[6, 974] [6, 2925] [6, 3243] [6, 5784] [6, 6030] [6, 7290] [6, 9885] [6, 10491] [6, 12528]

Contains 11 semigroups of order six

The semigroups of order six that satisfy the basis.

Show all 11