Finite Moufang loop

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Definition

A finite Moufang loop is a Moufang loop whose underlying set is a finite set.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Finite group

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Finite algebra loop
Algebra loop satisfying Lagrange's property