Originally Posted by

**Dreamer78692** Let f: G -> K be an epimorphism of groups. If N is a normal

subgroup of G, show that f(N) := {f(n) | n e N} is a normal subgroup of K.

please note in this proof "e" is the id for G

and "i" is the id for K

My proof:

Let g, h be an elements of G

Suppose N is a normal subgroup of G,

then f(e)=i is element of f(N)

f(g^(-1))= f(g)^(-1) is element of f(N)

f(g)f(h) = f(gh)=f(N)

therefore N is subgroup of K

Now to proof that it is a normal subgroup of K

f(ghg(-1))=f(g)f(h)f(g)^(-1)

Now im stuck...

Can some one please show me how to proof this , and if my proof that i gave so far

is incorrect plz show me how in the simplest way ...

Thank you in advance.