Divisible subgroups as exact equalizers in torsion-free nilpotent groups

Let \\(G\\) be torsion-free nilpotent of class at most \\(c\\), and let \\(H\\leq G\\) be divisible. We construct a torsion-free nilpotent group \\(K\\) of class at most \\(c\\) and embeddings \\(f_0,f_1:G\\hookrightarrow K\\) whose equalizer is exactly \\(H\\). Consequently the dominion of \\(H\\) in \\(G\\), relative to torsion-free nilpotent groups of class at most \\(c\\), is \\(H\\), answering Kourovka Problem 17.34. The construction uses the rational Mal'cev correspondence and a derivation into a truncated quotient of the augmentation ideal of a universal enveloping algebra. The augmentation filtration preserves the original nilpotency-class bound. No finite-generation or normality hypothesis on \\(H\\) is required.