Let \(G\) be a nilpotent group of class \(c\). For some natural number \(n\in\mathbb{N}\) depending on \(c\) only, the authors consider the subgroup \(G^n\). They use the Baker-Hausdorff formula and define the structure of a Lie ring \(M\) on \(G^n\) in such a way that many important parameters of \(M\) as a Lie ring are equal to those of \(G^n\) as a nilpotent group. For instance, the nilpotency class and the derived length of the Lie ring and the group coincide. The correspondence can be applied to any nilpotent group, including finite \(p\)-groups, but it is based on the subgroup \(G^n\). It is not so fruitful as the Mal'tsev correspondence.