Lagrange-like subloop

This article defines a property that can be evaluated for a subloop of a loop| View other such properties

Definition

A subloop of a finite algebra loop is termed a Lagrange-like subloop if the order (i.e., the number of elements) of the subloop divides the order of the loop.

Relation with other properties

• Algebra loop satisfying the weak Lagrange property is a finite algebra loop in which every subloop is Lagrange-like.
• Algebra loop satisfying the strong Lagrange property is a finite algebra loop in which every subloop satisfies the weak Lagrange property.