Generalized Lazard correspondence

The term generalized Lazard correspondence can be used for any of a number of possible generalizations of the Lazard correspondence, some of which are more general than others.

The Lazard correspondence (which we call the Lazard correspondence proper to distinguish it from generalizations) is a correspondence:

Lazard Lie rings $$\leftrightarrow$$ Lazard Lie groups

Here:


 * A Lazard Lie ring is a Lie ring such that there exists a natural number $$c$$ such that the additive group is powered over for all primes $$p \le c$$ and any subring generated by at most three elements is a nilpotent Lie ring of class at most $$c$$.
 * A Lazard Lie group is a group such that there exists a natural number $$c$$ such that the group is powered over for all primes $$p \le c$$ and any subgroup generated by at most three elements is a nilpotent Lie ring of class at most $$c$$.