Let K be a finite extension of Q_p with residue field F_q and let P(T) = T^d
+ a_{d-1}T^{d-1} + ... +a_1 T, where d is a power of q and a_i is in the
maximal ideal of K for all i. Let u_0 be a uniformizer of O_K and let {u_n}_{n
\geq 0} be a sequence of elements of Q_p^alg such that P(u_{n+1}) = u_n for all
n \geq 0. Let K_infty be the field generated over K by all the u_n. If K_infty
/ K is a Galois extension, then it is abelian, and our main result is that it
is generated by the torsion points of a relative Lubin-Tate group (a
generalization of the usual Lubin-Tate groups). The proof of this involves
generalizing the construction of Coleman power series, constructing some p-adic
periods in Fontaine's rings, and using local class field theory.Comment: 15 pages; v2: some edits for clarity, and in the title "iterate" has
been changed to "iterated
