21.42 (2026)

Let $T_{d,c}$ denote the class of $d$-generated, torsion-free nilpotent groups having class $c$. It is known that $T_{d,2}$-groups are self-similar for all $d$, that $T_{2,3}$-groups are self-similar, and that there are $T_{4,3}$-groups that are not self-similar (A. Berlatto, T. Santos, Preprint, 2025, https://arxiv.org/abs/2509.16947). Are there $T_{3,3}$-groups that are not self-similar? (See 21.41 for the definition of self-similarity.)