Global UCS-Lazard Lie group

Definition
A group is termed a global UCS-Lazard Lie group if there exists a positive integer $$c$$ such that both the following two conditions hold:


 * 1) The group is a nilpotent group of nilpotency class less than or equal to $$c$$.
 * 2) For any positive integer $$i$$ with $$i \le c$$, the upper central series member $$Z^i(G)$$ is powered over all the primes less than or equal to $$c + 1 - i$$.