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# 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.