\begin{definition}[Definition:Latin Square Property]
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:
:$\forall a, b \in S: \exists ! x: x \circ a = b$
:$\forall a, b \in S: \exists ! y: a \circ y = b$
\end{definition}