# Group homomorphisms between cyclic groups

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.

## Answers and Replies

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

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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.