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 |