Hi,

I was wondering if someone could help me with this question I have.

"Iff: G--> H is a homomorphism, prove the following. "If the range offhasnelements, thenxis in the kern^{n}ffor everyxin G. ""

I know that the kernfis a set K that has all elements of G that are carried byfonto the neutral element in H.

I also know that the range offis 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 powernwherenis the number of elements in the range, then all of those x^{n}must be mapped to the neutral element of H. Is that correct?

Any help is greatly appreciated!

Thanks!