I read somewhere that a small cancellation group (ie. a group admitting a presentation statisfying the small cancellation condition $C'(1/6)$) does not contain $\mathbb{Z}^3$, but without a precise reference. Do you know a reference containing a proof of the above statement?
Similarly, in hyperbolic groups, $\mathbb{Z}^2$ is a forbidden subgroup: it may be seen as a consequence of a more general result on centralizers. Does there exist a similar property on centralizers in small cancellation groups?