A group (G,*) is a structure composed of a set of elements in the set G and a binary operation * defined on G X G onto G .The operation must meet some conditions .The operation must have closure,identity,inverses and associativity.
closure
For every pair of elements f,g not necessarly distinct and elements of the set G If f*g=h then h is also a element of G.
identity
There exists a unique element in G which we shall call i such that for any element g of G then g*i=g.
inverses
For all g an element of G there exists an element f in G such that g*f=i and we shall call f the inverse of g or g'.
associativity
For every triplet of elements f,g,h not necessarly distinct and elements of the set G then f*(g*h)=(f*g)*h