Loop satisfying the weak Lagrange property

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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