G-loop

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

This is a variation of group|Find other variations of group | Read a survey article on varying group

Definition

A loop is termed a G-loop if every loop isotopic to it (as a magma with the multiplicative structure; the isotopy will automatically transform the left and right quotient operations accordingly) is in fact isomorphic to it.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Group		group implies G-loop	G-loop not implies group	|FULL LIST, MORE INFO