On the nilpotency of rational $\bm{H}$-spaces

Abstract

In [BG], it is proved that the Whitehead length of a space $Z$ is less than or equal to the nilpotency of $\mathrm{\Omega }Z$. As for rational spaces, those two invariants are equal. We show this for a 1-connected rational space $Z$ by giving a way to calculate those invariants from a minimal model for $Z$. This also gives a way to calculate the nilpotency of an homotopy associative rational $H$-space.