High Quality Content by WIKIPEDIA articles! 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. 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.

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