Extra loop

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

Definition

An loop (L,*) is termed an extra loop if it satisfies the following identity for all x,y,z \in L:

\! x * (y * (z * x)) = ((x * y) * z) * x

Relation with other properties

Stronger properties

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

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Moufang loop
C-loop
Left Bol loop
Right Bol loop
Flexible loop
Left alternative loop
Right alternative loop