This is certainly a small step towards a satisfactory answer, but in the case of the solvable Baumslag-Solitar group $BS(1, n) = \langle a, b \, \vert \, aba^{-1} = b^n \rangle$ with $n \in \mathbb{Z} \setminus \{0\}$, anything can happen within its unique $T_2$-system. This preprint presents of proof of my claim, see Corollary E.
Luc Guyot
- 7.9k
- 2
- 30
- 51