# Category:Quasigroups

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This category contains results about **Quasigroups**.

Definitions specific to this category can be found in Definitions/Quasigroups.

A **quasigroup** is a magma $\struct {S, \circ}$ which has the Latin square property.

That is, such that $\forall a \in S$, the left and right regular representations $\lambda_a$ and $\rho_a$ are permutations on $S$.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Quasigroups"

The following 12 pages are in this category, out of 12 total.

### C

### S

- Self-Distributive Quasigroup is Idempotent
- Self-Distributive Quasigroup with at least Two Elements has no Identity
- Self-Distributive Quasigroup with at least Two Elements is not Associative
- Structure Induced by Permutation on Commutative Quasigroup is Commutative Quasigroup
- Structure Induced by Permutation on Quasigroup is Quasigroup
- Structure is Group iff Semigroup and Quasigroup