Mathematics

# Group

Group:

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.