The primitive-unipotent conjecture for linear groups

Let $G\subseteq GL(n,\mathbb{C})$ be a finitely generated subgroup. An element of $G$ is primitive if it belongs to a generating set obtainable from the fixed generating set by finitely many Schreier transformations, and an element is unipotent if all its eigenvalues are equal to $1$. Primitive-unipotent conjecture. If all primitive elements of $G$ are unipotent, then $G$ is nilpotent. This folklore conjecture generalizes related conjectures studied by Platonov and Potapchik; its resolution is not specified in the source.