There are much easier examples than Tarski Monsters! For example, fix a prime $p$, and take the multiplicative group of complex $p^n$-th roots of unity for all $n \ge 0$.
– Derek HoltOct 27 '12 at 12:10

Of course, the group mentioned by Derek is just the Prufer group.
– Salvatore SicilianoOct 27 '12 at 22:42

Yes but the Tarski monsters were the first known finitely generated examples. It is
open whether there exist finitely presented groups with this property.

Yes but there was no request for a finitely generated example! I suspect that you are just trying to make an easy question more interesting (which is of course not unreasonable)!
– Derek HoltOct 27 '12 at 13:11