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

  1. Sep 4, 2009 #1
    1. The problem statement, all variables and given/known data
    Find all group morphism from ( Z,+) to (Q, +)


    2. Relevant equations
    None

    3. The attempt at a solution
    I think the identity morphism is included, but I'm not sure what else
     
  2. jcsd
  3. Sep 4, 2009 #2

    Hurkyl

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    Don't you know a lot about homomorphisms whose domain is (Z,+)?
     
  4. Sep 4, 2009 #3
    Well I think the trouble I'm having is finding all of them
     
  5. Sep 4, 2009 #4

    Hurkyl

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    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.
     
  6. Sep 4, 2009 #5
    f(n)=cn

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

    thanks for the help!
     
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