# Commutative Moufang loop

From Groupprops

This article defines a property that can be evaluated for a loop.

View other properties of loops

## Contents

## Definition

A **commutative Moufang loop** or **abelian Moufang loop** is a Moufang loop that is also a commutative loop.

## Relation with other properties

### Stronger properties

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

abelian group |

### Weaker properties

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

Moufang loop | |FULL LIST, MORE INFO | |||

commutative loop | |FULL LIST, MORE INFO |