In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that they need not be associative.A quasigroup with an identity element is called a loop. Definitions There are two equivalent formal definitions of quasigroup with, respectively, one and three primitive binary operations. We begin with the first definition, which is easier to follow. A quasigroup &la… (More on Quasigroup)