Groups:

Binary composition:

Let A be a non-empty set. A binary composition (a binary operation) on A is a mapping

Definition:

Let * be a binary composition on a set A.
* is said to be commutative if a*b=b*a for all a,b belongs to A.
* is said to be associative if a*(b*c)=(a*b)*c for all a,b,c belongs to A.

Example:

Addition on Real number is both commutative and associative.

Composition table:

If a set A be finite there any composition on A can be represented by composition table. For example let a set A represent (1,w,w^2) and the composition be taken as '.' that is usual multiplication. Then the composition table be written as follows :