G-loop

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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 Flexible G-loop|FULL LIST, MORE INFO