Definition:Latin Square Property

Definition
Let $\left({S, \circ}\right)$ be an algebraic structure.

$\left({S, \circ}\right)$ has the Latin square property iff:
 * $\forall a \in S$, the left and right regular representations $\lambda_a$ and $\rho_a$ are permutations on $S$.

That is:
 * $\forall a, b \in S: \exists ! x: x \circ a = b$
 * $\forall a, b \in S: \exists ! y: a \circ y = b$

Also see

 * Definition:Quasigroup