homomorphisms

Introduction
After we studied the concept of group now we will study the concept of the homomorphism and isomorphism and kernel .
A homomorphism is a function from the group ( G , * ) into the group ( G / , * / ) such that for
each a and b in G
f ( a * b ) = f ( a ) * / f ( b ) .

A kernel of f is denoted by ker ( f ) ,
Ker ( f ) = { a ? G | f ( a ) = e/ } .
If f is a homomorphism function
Then
1 - F ( e ) = e /
2 - f ( a ) – 1 = f ( a – 1 )