Can someone guide me through the proof (or point me to where I can find the proof) that the group of rational numbers is not finitely generated?(adsbygoogle = window.adsbygoogle || []).push({});

I know that it helps to break it into steps, the first of which you show that any finitely generated subgroup of Q is contained in a cyclic subgroup (and hence is cyclic), and in the second step you show that Q itself is not cyclic.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Q not finitely generated

**Physics Forums | Science Articles, Homework Help, Discussion**