A group in mathematics has the following properties:
There exist a set of elements p, q, r, … and a binary operation which applied to p, q gives pq.
The set is closed under this single-valued operation.
- The associative law: p(qr) = (pq)r.
- Identity law: p i = i p.
- Inverse law: there exist p’ such that p p’ = p’ p
If the group axioms are full-filled i is unique and the inverse is also unique.