Equation 677 Database

Can we find a finite magma M that satisfies

∀ x y : M,   x = y ◇ (x ◇ ((y ◇ x) ◇ y)) (Equation 677)

but does not satisfy

∀ x : M,   x = ((x ◇ x) ◇ x) ◇ x  ? (Equation 255)

This site collects finite magmas that satisfy Equation 677. So far, every known example also satisfies Equation 255 — finding one that does not (or proving none exists) is the main open question remaining from the Equational Theories Project.

The canonicalization and database are based on memoryleak47/eq677.

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magma 640446bd of size 781 magma bef86252 of size 65 magma 5a221b8b of size 35 magma 2d0e5a3f of size 385

(random magmas from the database)

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Paste a Cayley table: n rows, each with n non-negative integers < n, whitespace- or comma-separated. A JSON array of arrays (e.g. [[0,1],[1,0]]) is also accepted.