I need to show that $\displaystyle \mathbb{Q} \times Z_2$ is not isomorphic to $\displaystyle \mathbb{Q}$.

Mind you, I'm in the section of my book dealing with cyclic groups. I was able to handle the other problems in this set by showing that one group is cyclic and the and the other isn't, etc. But $\displaystyle \mathbb{Q}$ isn't cyclic and I don't see how $\displaystyle \mathbb{Q} \times Z_2$ would be either. Any thoughts?

Thanks!

-Dan