Size 2

0 isomorphism classes.

No magmas of this size are in the database yet.

Commentary

No magma of size 2 satisfies Equation 677. Proof. Equation 677, x = y ◇ (x ◇ ((y ◇ x) ◇ y)), implies that for each fixed y, the map z ↦ y ◇ z is a bijection: its inverse sends x to x ◇ ((y ◇ x) ◇ y). So every row of the Cayley table must be a permutation of the carrier. An exhaustive check of all 2² = 4 such 2×2 row-Latin tables shows that none satisfies Eq677. [text written by Claude]

last edited by dwrensha at 2026-05-14 19:45:18 · history