groups

Introduction
After we studied the concept of semigroup with identity
Element , now we will study the concept of the group .
A group is a pair ( G , ? ) consisting of a nonempty set G
and a binary operation ? defined on G , satisfying :
1) G is closed under the operation ? ,
2) the operation? is associative ,
3) G contains an identity element e for the operation ?,and
4) each element a of G has an inverse a -1?G , relative to ? .
In this lecture , we will prove that each element of a
Group has only one inverse