Find all group morphism from ( Z,+) to (Q, +)

[polarbears]

Homework Statement

Find all group morphism from ( Z,+) to (Q, +)

Homework Equations

None

The Attempt at a Solution

I think the identity morphism is included, but I'm not sure what else

 

[Hurkyl]

Don't you know a lot about homomorphisms whose domain is (Z,+)?

 

[polarbears]

Well I think the trouble I'm having is finding all of them

 

[Hurkyl]

Which is why you need to consider what facts you know about homomorphisms from (Z,+)!

Surely you know some useful theorem about homomorphisms from free Abelian groups?

And if not, you could look find some easy way to describe any such homomorphism, and maybe this description would make it easy to identify all of them.

 

[polarbears]

f(n)=cn

wow that was pretty obvious...I need some rest

thanks for the help!