[Thanks to Alar Leibak, aleibak@ioc.ee, for helping to construct this page]

## Definition

- A
quasigroup where
*xy=z*implies the following equalities:*yx=z, xz=y, zx=y, yz=x*and*zy=x* - A
quasigroup satisfying
*xy=yx*and*x(xy)=y*

- A
quasigroup where
## Examples

- Every Steiner quasigroup

## Structure

## Representation

## Decision problems

**Identity problem**:**Word problem**:## Spectra and growth

**Finite spectrum****:****Free spectrum****:****Growth series****:****History/Importance****References****V. D. Belousov,***Fundamentals of the theory of quasigroup and loop*(*in Russian*)**Subsystems**