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The results of Theorems 2.3 and 2.6 have also been obtained independently by David M. Riley [Restricted Lie dimension subgroups, Comm. Algebra (to appear)].
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Bhandari, A.K., Passi, I.B.S. Residually Lie nilpotent group rings. Arch. Math 58, 1–6 (1992). https://doi.org/10.1007/BF01198635
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DOI: https://doi.org/10.1007/BF01198635