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Math Help - [SOLVED] Proper Subgroups of Q

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    Member Haven's Avatar
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    [SOLVED] Proper Subgroups of Q

    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.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Haven View Post
    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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