Loop satisfying the strong Lagrange property
This article defines a property that can be evaluated for a loop.
View other properties of loops
Definition
A finite loop is said to satisfying the strong Lagrange property if every subloop of the loop satisfies the weak Lagrange property, i.e., the order of any subloop of the subloop divides the order of the subloop.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Finite group | Lagrange's theorem | |FULL LIST, MORE INFO | ||
| Finite Moufang loop | every finite Moufang loop satisfies the strong Lagrange property | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Algebra loop satisfying the weak Lagrange property | |FULL LIST, MORE INFO |