Group homomorphisms between cyclic groups

Describe al group homomorphisms [tex] \phi [/tex] : [tex] C_4 [/tex] --> [tex] C_6 [/tex]

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 [tex]\phi[/tex] (a*b) = [tex]\phi[/tex] (a) * [tex]\phi[/tex] and that it maps the inverses to the inverses but I just have no idea how to apply these.
 
I forgot a b in the definition of phi(a*b) = phi(a)*phi(b)
 

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

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