# Loop satisfying the weak Lagrange property

From Groupprops

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

View other properties of loops

## Definition

An finite loop is said to satisfy the **weak property** if every subloop is a Lagrange-like subloop, i.e., the order (number of elements) of any subloop divides the order of the loop.

## Relation with other properties

### Stronger properties

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

Finite group | Lagrange's theorem | Finite Moufang loop, Loop satisfying the strong Lagrange property|FULL LIST, MORE INFO | ||

Finite Moufang loop | every finite Moufang loop satisfies the weak Lagrange property | Loop satisfying the strong Lagrange property|FULL LIST, MORE INFO | ||

Loop satisfying the strong Lagrange property | every subloop satisfies the weak Lagrange property | |FULL LIST, MORE INFO |