[SOLVED] Proper Subgroups of Q

Printable View

February 1st 2010, 11:28 AM
Haven

[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.
February 1st 2010, 12:26 PM
Drexel28

Quote:

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

All times are GMT -8. The time now is 03:19 PM.

Copyright © 2005-2013 Math Help Forum. All rights reserved.

Copyright © 2005-2013 Math Help Forum. All rights reserved.