The torsion-group conjecture for associated Lie algebras

Let $G$ be a group, and let its associated Lie algebra be defined from the relevant group-theoretic filtration. Torsion-group conjecture. If $G$ is a torsion group, then its associated Lie algebra is nil. This would connect torsion phenomena in groups with nilpotence properties of their associated Lie algebras; the supplied text does not indicate whether the assertion has been proved or disproved.