Loop satisfying the strong Lagrange property

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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