Hi all,

As a homework, I've been asked to find whether there is or not an infinite group such that all of its proper subgroups are finite.

I've been told to consider {m/2^n, m,n integers, 0<=m/2^n<1} with mod1 addition. It's not very hard to show that it's an infinite group, but I can't see how (for example) G\{1/2} could be a finite group, let alone showing that all of G's subgroups are finite...

Can anyone help me? Thank you!