p-adic period map for the moduli space of deformations of a formal group

The moduli space of deformations of a formal group over a finite field is studied. We consider Lubin-Tate and Dieudonné approaches and find an explicit relation between them employing Hazewinkel's universal p-typical formal group, Honda's theory and rigid power series. The formula obtained allows to give an explicit description of the action of the automorphism group of the formal group on the moduli space. It essentially generalizes an analogous result of Gross and Hopkins [Contemp. Math. 158 (1994) 23-88].