I was told that a polynomial group law on (all of) $\mathbb{R}^n$ gives automatically a nilpotent (Lie, of course) group. 


Is it true? Where can I find a proof?


A counterexample for open subsets of $\mathbb{R}^n$ is furnished by the halfplane with the $ax+b$ law. 



Is a polynomial group law on $\mathbb{R}^n$ automatically nilpotent?
This is true and is in "Michel Lazard: Sur la nilpotence de certains groupes algébriques, Comptes Rendus, vol 241, 1955, 1687--1689"


