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.
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.