Platonov–Potapchik's primitive-unipotent conjecture

Let $G=\langle S\rangle$ be a group with a fixed finite generating set $S$. An element of $G$ is primitive if it occurs in a generating set obtained from $S$ by finitely many Schreier transformations, and an element is unipotent if all its eigenvalues are equal to $1$.

Platonov–Potapchik's conjecture. If all primitive elements of $G$ are unipotent, then the group $G$ generated by $S$ is unipotent.

The conjecture is presented as a general question posed by Platonov and Potapchik; the cited theorem gives only a partial answer in a representation-theoretic setting. Its resolution is not specified in the source.