The main result in this paper is the following: Let G be a torsion-free locally nilpotent group and let F be a finitely generated subgroup of G. If every subgroup of G containing F is subnormal in G, then G is nilpotent.
ÖZEN, TAHİRE (2004) "A Generalization of a Result on Torsion-Free Groups With all Subgroups Subnormal," Turkish Journal of Mathematics: Vol. 28: No. 4, Article 5. Available at: https://journals.tubitak.gov.tr/math/vol28/iss4/5