Lagrange-like subloop

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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 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

Stronger properties

All the properties below are stronger conditional to the ambient loop being finite.

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
direct factor of a loop Central factor of a loop|FULL LIST, MORE INFO
central factor of a loop |FULL LIST, MORE INFO
central subloop Central factor of a loop|FULL LIST, MORE INFO
cocentral subloop |FULL LIST, MORE INFO
normal subloop normal implies Lagrange-like |FULL LIST, MORE INFO
subnormal subloop |FULL LIST, MORE INFO