loop and quasigroup

A quasigroup is a groupoidPlanetmathPlanetmathPlanetmathPlanetmath G with the property that for every x,yG, there are unique elements w,zG such that xw=y and zx=y.

A loop is a quasigroup which has an identity elementMathworldPlanetmath.

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