19.23 (2018)

For a group $G$, let $\text{Tor}_1(G)$ be the normal closure of all torsion elements of $G$, and then by induction let $\text{Tor}_{i+1}(G)$ be the inverse image of $\text{Tor}_1(G/\text{Tor}_i(G))$. The torsion length of $G$ is defined to be either the least positive integer $l$ such that $G/\text{Tor}_l(G)$ is torsion-free, or $\omega$ if no such integer exists (since $G/\bigcup \text{Tor}_i(G)$ is always torsion-free).

Does there exists a finitely generated, or even finitely presented, soluble group with torsion length greater than 2?