# divisible group + monomorphism

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• Mar 23rd 2011, 07:38 AM
alper82
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.
• Mar 23rd 2011, 12:11 PM
alper82
any proof?
• Mar 23rd 2011, 01:39 PM
Drexel28
Quote:

Originally Posted by alper82
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 $|g|=\infty$...
• Oct 7th 2011, 12:47 AM
alper82
Re: divisible group + monomorphism
Any idea please?
• Oct 7th 2011, 01:37 AM
Swlabr
Re: divisible group + monomorphism
Quote:

Originally Posted by alper82
Any idea please?

What about Drexel's idea do you not understand?
• Oct 7th 2011, 04:17 AM
alper82
Re: divisible group + monomorphism
Yes i know it already. But i dont know how can i build a homomorphism from Q to D.
• Oct 7th 2011, 06:22 AM
Deveno
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....