Prove or Disprove: Any proper subgroup of $\displaystyle G = (\mathbb{Q},+)$ is cyclic.

I want to say for any $\displaystyle H \subseteq \mathbb{Q}, H = k\mathbb{Q}$ for some $\displaystyle k \in \mathbb{Q}$ but I'm not sure how to prove it.

Printable View

- Feb 1st 2010, 11:28 AMHaven[SOLVED] Proper Subgroups of Q
Prove or Disprove: Any proper subgroup of $\displaystyle G = (\mathbb{Q},+)$ is cyclic.

I want to say for any $\displaystyle H \subseteq \mathbb{Q}, H = k\mathbb{Q}$ for some $\displaystyle k \in \mathbb{Q}$ but I'm not sure how to prove it. - Feb 1st 2010, 12:26 PMDrexel28