If f Sn Sn is a homomorphism prove that fAn is a subset of A

If f: Sn--- Sn is a homomorphism, prove that f(An) is a subset of An.

Solution

Given f : S_n ---> S_n is a homomorphism

Let S_{n =} A == { a,b , c , -------} their images are B= f(S_n)= { f(a) ,f(b) , f(c) -----}

the elements of B arethe elements of A .

If f is an isomorphism then it is an one - one fn .in that case B =A

if f is not a one - one fn then B is a Subset Of A