[SOLVED] Proper Subgroups of Q

**Haven** · February 1st 2010, 11:28 AM

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

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

**Drexel28** · February 1st 2010, 12:26 PM

Originally Posted by Haven

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

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

Try $K\leqslant \mathbb{Q}$ where $K=\left\{\frac{k}{2^{\ell}}:k,\ell\in\mathbb{Z}\ri ght\}$

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