Quasigroup

A quasigroup (Q, *) is a set Q with a binary operation * (that is, a magma), such that for each a and b in Q, there exist unique elements x and y in Q such that:

• a * x = b ;
• y * a = b .

(In other words: For two elements a and b, b can be found in row a and in column a of the quasigroup's Cayley table. So the Cayley tables of quasigroups are simply latin squares.)
The unique solutions to these equations are written x = a \ b and y = b / a. The operations '\' and '/' are called, respectively, left and right division.