A groupoid S such that for all a, b element S, there exist unique x, y element S such that a x | = | b y a | = | b. No other restrictions are applied; thus a quasigroup need not have an identity element, not be associative, etc. Quasigroups are precisely groupoids whose multiplication tables are Latin squares. A quasigroup can be empty.

algebraic loop | binary operator | groupoid | Latin square | monoid | semigroup