Quasigroup

https://en.wikipedia.org/wiki/Quasigroup

• Quasigroup resembles a group, i.e. "division" is always possible

• unlike groups, they are not necessarily associative

• Loop is a quasigroup with an identity element

There are at least two structurally equivalent formal definitions: 1. a set with one binary operation 2. (from universal algebra) 3 primitive operations

The homomorphic image of a quasigroup defined with a single binary operation, however, need not be a quasigroup.