# Finite Moufang loop

From Groupprops

## Contents

## Definition

A **finite Moufang loop** is a Moufang loop whose underlying set is a finite set.

## Relation with other properties

### Stronger properties

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

Finite group |

### Weaker properties

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

Finite algebra loop | ||||

Algebra loop satisfying Lagrange's property |