Homomorphism from $\mathbb{Q}/ \mathbb{Z}\rightarrow \mathbb{Z}/n\mathbb{Z}$ Let $\mathbb{Q}$ be the group ($\mathbb{Q}$,+) and $\mathbb{Z}$ is a sub-group of $\mathbb{Q}$.
It is quite easy to find all homomorphism from $\mathbb{Z}/n\mathbb{Z}\rightarrow \mathbb{Q}/ \mathbb{Z}$.
However, I couldn't find what would be all  homomorphism from $\mathbb{Q}/ \mathbb{Z}\rightarrow \mathbb{Z}/n\mathbb{Z}$.
Please help me.

Another approach:
As a homomorphic image of a divisible group, the quotient $\;\Bbb Q/\Bbb Z\;$ is divisible, and thus the image of any homomorphism from this group is also divisible. But the only divisible finite group is the trivial one, and thus the only possible homomorphism $\;\Bbb Q/\Bbb Z\to\Bbb Z/n\Bbb Z\;$ is the trivial one.
