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.