3-additive Lazard Lie cring

Definition
A 3-additive Lazard Lie cring is defined as a defining ingredient::3-additive Lie cring such that there exists a nonnegative integer $$c$$ satisfying the following:


 * The Lie cring is 3-locally a nilpotent Lie cring of nilpotency class $$c$$ (i.e., any three elements generate a nilpotent subcring of class at most $$c$$)
 * The additive group of the Lie cring is uniquely $$p$$-divisible for all odd primes $$p \le c$$.

A 3-additive Lazard Lie cring can be the intermediate object to pass between Lie rings and groups in what's called the 3-additive Lie cring generalization of Lazard correspondence.