Homomorphism: Abstract Algebra?

Question

Why can't there be a homomorphism from Z_16 onto Z_2 (+) Z_2?

Note: (+) means external direct product

Answer 1

The first poster is wrong because the word "onto" means that we're talking about surjective homomorphisms in this context. So imagine what would happen if we had a surjective homomorphism f: Z_16 -> Z_2^2. There would be some x in Z_16 such that f(x) = (0, 1), and some y in Z_16 such that F(y) = (1, 0). Then...

Answer 2

there are:
f(x) = 0 is a homomorphism