__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.

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