Definition:Quasigroup

Definition
A quasigroup is a magma $\struct {S, \circ}$ which has the Latin square property.

That is, such that $\forall a \in S$, the left and right regular representations $\lambda_a$ and $\rho_a$ are permutations on $S$. That is:
 * $\forall a, b \in S: \exists ! x: x \circ a = b$
 * $\forall a, b \in S: \exists ! y: a \circ y = b$