About the Zassenhaus’s filtration of a group G

The $ n$ -th term of the filtration of Zassenhaus of a group $ G$ , denoted by $ D_n(G)$ , is the subgroup generated by all $ p^k$ -th power of an element $ x\in \gamma_i(G)$ such that $ ip^k$ is greater or equal $ n$ . In a text by Zelmanov, i saw that we can get the subgroup $ D_n(G)$ using the same powers but only of the simple commutators in $ G$ .

Can anyone explain me how to get this or tell me a reference (book or article) that contains the proof of this statement?