# Extra loop

This article defines a property that can be evaluated for a loop.
View other properties of loops

## Definition

An loop $(L,*)$ is termed an extra loop if it satisfies the following identity for all $x,y,z \in L$:

$\! x * (y * (z * x)) = ((x * y) * z) * x$

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Group

### Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Moufang loop
C-loop
Left Bol loop
Right Bol loop
Flexible loop
Left alternative loop
Right alternative loop