Loop satisfying the weak Lagrange property

This article defines a property that can be evaluated for a loop.
View other properties of loops

Definition

An algebra loop is said to satisfy the weak property if it is finite (i.e., its underlying set is finite) and 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		|FULL LIST, MORE INFO
Finite Moufang loop		every finite Moufang loop satisfies the weak Lagrange property		|FULL LIST, MORE INFO
Algebra loop satisfying the strong Lagrange property	every subloop satisfies the weak Lagrange property			|FULL LIST, MORE INFO