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

抄録

In \cite{BG}, it is proved that the Whitehead length of a space Z is less than or equal to the nilpotency of \varOmega 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.