Loop satisfying the weak Lagrange property
This article defines a property that can be evaluated for a loop.
View other properties of loops
An algebra loop is said to satisfy Lagrange's property if it is finite (i.e., its underlying set is finite) and the order (i.e., size) of any subloop of the algebra loop divides the order (i.e., size) of the whole algebra loop.
Relation with other 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 Lagrange's property||Loop satisfying the strong Lagrange property|FULL LIST, MORE INFO|