# G-loop

From Groupprops

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 |