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Homeloop and quasigroup

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# 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.

Defines:

loop, quasigroup

Related:

Groupoid, , LoopOfAGraph, AlternativeDefinitionOfGroup

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

20N05*no label found*

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