I was wondering if someone could help me with this question I have.
"If f: G--> H is a homomorphism, prove the following. "If the range of f has n elements, then xn is in the kern f for every x in G. ""
I know that the kern f is a set K that has all elements of G that are carried by f onto the neutral element in H.
I also know that the range of f is a subgroup of H.
So what the question is asking to prove is that if we take every element of G and raise it to the power n where n is the number of elements in the range, then all of those xn must be mapped to the neutral element of H. Is that correct?
Any help is greatly appreciated!