Lower central series of a Lazard-divided Lie ring

Definition
Suppose $$L$$ is a Lazard-divided Lie ring. Its lower central series is defined as follows: the $$k^{th}$$ member $$\gamma_k(L)$$ is the Lazard-divided Lie subring generated by all products of length $$k$$, where the product may compose the Lie bracket and one or more of the Lazard division operations.