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
Canonical name	LoopAndQuasigroup
Date of creation	2013-03-22 13:02:08
Last modified on	2013-03-22 13:02:08
Owner	mclase (549)
Last modified by	mclase (549)
Numerical id	4
Author	mclase (549)
Entry type	Definition
Classification	msc 20N05
Related topic	Groupoid
Related topic	LoopOfAGraph
Related topic	AlternativeDefinitionOfGroup
Defines	loop
Defines	quasigroup