On the norm maps of formal groups for Zp-extensions

Let K be a finite extension of Qp and F(X,Y) be a formal group defined over OK where OK is the ring of integers of K. For an arbitrary Zp-extensions K∞/K and the nth layer Kn, we study the index [F(Kn-1):F-NKn/Kn-1(F(Kn))]. We give the asymptotic behavior of the index as n→∞, and determine the index in several cases.