Group homomorphisms between cyclic groups

[Gott_ist_tot]

Describe al group homomorphisms $$\phi$$ : $$C_4$$ --> $$C_6$$

The book I study from seems to pass over Group Homomorphisms very fast. So I decided to look at Artin's to help and it uses the same definition. So I think I am just not digesting something I should be. I know it's defined as $$\phi$$ (a*b) = $$\phi$$ (a) * $$\phi$$ and that it maps the inverses to the inverses but I just have no idea how to apply these.

 

[Gott_ist_tot]

I forgot a b in the definition of phi(a*b) = phi(a)*phi(b)

 

[StatusX]

If you specify $\phi(1)$, then what does this say about the value of $\phi$ at the other elements in C_4? Also, a general fact about homomorphisms is that the order of $\phi(g)$ must divide the order of g. Can you prove this? By the way, you can edit posts.