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 |
