quasigroup
Sign in to saveIn mathematics, especially in abstract algebra, a quasigroup is an algebraic structure that resembles a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that the associative and identity element properties are optional. In fact, a nonempty associative quasigroup is a group.
Article
28 sectionsContents
- Definitions
- Algebra
- Universal algebra
- Loops
- Symmetries
- Semisymmetry
- Triality
- Total symmetry
- Total antisymmetry
- Examples
- Properties
- Multiplication operators
- Latin squares
- Infinite quasigroups
- Inverse properties
- Morphisms
- Homotopy and isotopy
- Conjugation (parastrophe)
- Isostrophe (paratopy)
- Generalizations
- Polyadic or multiary quasigroups
- Number of small quasigroups and loops
- See also
- Notes
- References
- Citations
- Sources
- External links
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure that resembles a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that the associative and identity element properties are optional. In fact, a nonempty associative quasigroup is a group.
A quasigroup that has an identity element is called a loop.