LC-loop

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

Definition

An algebra loop $(L,*)$ is termed a LC-loop if it satisfies the following identity for all $x,y,z\in L$:

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

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
C-loop
Extra loop				|FULL LIST, MORE INFO
Group				|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Left alternative loop		LC implies left alternative
Left nuclear square loop		LC implies left nuclear square
Middle nuclear square loop		LC implies middle nuclear square