divisible group + monomorphism

**alper82** · March 23rd 2011, 06:38 AM

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.

**alper82** · March 23rd 2011, 11:11 AM

any proof?

**Drexel28** · March 23rd 2011, 12:39 PM

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 $|g|=\infty$ ...

**alper82** · October 6th 2011, 11:47 PM

Any idea please?

**Swlabr** · October 7th 2011, 12:37 AM

Originally Posted by alper82

Any idea please?

What about Drexel's idea do you not understand?

**alper82** · October 7th 2011, 03:17 AM

Yes i know it already. But i dont know how can i build a homomorphism from Q to D.

**Deveno** · October 7th 2011, 05:22 AM

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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