# loop and quasigroup

A quasigroup is a groupoid $G$ with the property that for every $x,y\in G$, there are unique elements $w,z\in G$ such that $xw=y$ and $zx=y$.

A loop is a quasigroup which has an identity element.

What distinguishes a loop from a group is that the former need not satisfy the associative law.

Title loop and quasigroup LoopAndQuasigroup 2013-03-22 13:02:08 2013-03-22 13:02:08 mclase (549) mclase (549) 4 mclase (549) Definition msc 20N05 Groupoid LoopOfAGraph AlternativeDefinitionOfGroup loop quasigroup