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Math Help - divisible group + monomorphism

  1. #1
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    Unhappy divisible group + monomorphism

    Prove that, If a divisible group D has a nonzero and infinite order element then there exist a monomorphism f:Q--->D .

    plese help me for this question. Thanks.
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  2. #2
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    any proof?
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by alper82 View Post
    Prove that, If a divisible group D has a nonzero and infinite order element then there exist a monomorphism f:Q--->D .

    plese help me for this question. Thanks.
    For every m\in\mathbb{Z} and n\in\mathbb{N} there exists some y\in G if ny=g^m where |g|=\infty...
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  4. #4
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    Re: divisible group + monomorphism

    Any idea please?
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  5. #5
    MHF Contributor Swlabr's Avatar
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    Re: divisible group + monomorphism

    Quote Originally Posted by alper82 View Post
    Any idea please?
    What about Drexel's idea do you not understand?
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  6. #6
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    Re: divisible group + monomorphism

    Yes i know it already. But i dont know how can i build a homomorphism from Q to D.
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  7. #7
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    Re: divisible group + monomorphism

    hmmm.... i have an integer m, and a natural number n. how can i make a rational number from that? i wonder....
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