Let G=Z4, the group of integers modulo 4, and let H be the Klein four group, let f: G->H be a homomorphism. Why does the kernel of f must contain the element of 2 of G?
I do not have enough rep for voting to delete. I am mentioning this for users who have this privilege. (This can help to clean up the frontpage. Since the OP has already been directed elsewhere, I see no harm in removing the question.)
