LCS-Lazard Lie group

Definition
A LCS-Lazard Lie group is a group $$G$$ satisfying both the following properties:


 * 1) It is a 3-locally nilpotent group, i.e., any three elements of the group generate a nilpotent subgroup.
 * 2) Its defining ingredient::3-local lower central series powering threshold is $$\infty$$. Explicitly, for any nonnegative integer $$k$$, let $$\gamma_k^{3-loc}(G)$$ denote the $$k^{th}$$ member of the defining ingredient::3-local lower central series of $$G$$. Then, $$\gamma_k^{3-loc}(G)$$ is powered over all the primes $$p \le k$$.

The definition of LCS-Lazard Lie group is somewhat nicer than the definition of Lazard Lie group in that it does not involve a "nilpotency class-specific definition."