# Multiary quasigroup

From Groupprops

## Definition

A **multiary quasigroup** or **polyadic quasigroup** is a -ary quasigroup for some . Note that the case corresponds to the usual notion of quasigroup.

A -ary quasigroup is defined as a set with a -ary operation, i.e., a map such that the equation has a unique solution with any as the unknown and all other quantities (i.e., all the other <mah>a_j</math>s and ) known.

## Related notions

- Multiary semigroup
- Multiary group is something that's both a multiary quasigroup and a multiary semigroup