A group is an ordered pair (G, *) where G is a non empty set and ‘*’ is a binary operation in G satisfying the following conditions:
(i) CLOSURE LAW:
For all a, b ϵG , a*b ϵ G
(ii) ASSOCIATIVE LAW:
For all a, b ϵG , then a*(b*c) = (a*b)*c
(iii) EXISTENCE OF IDENTITY:
For all a, b ϵG ,there exists an element e ϵ G such that a * e = e * a = a, where e is the identity element.
(iv) EXISTENCE OF INVERSE:
For all a ϵG, there exists an element a-1 ϵG such that a * a-1 = a-1 * a = e , where a-1 is called the inverse of a.