Galois groups of some iterated polynomials over cyclotomic extensions

Abstract

Let ϕ p (z) = (z − 1) p + 2 − ζ p , where ζ p ∈ Q is a primitive p-th root of unity for some odd prime p. Building on previous work, we show that the n-th iterate ϕ n p (z) has Galois group [C p ] n , an iterated wreath product of cyclic groups, whenever p is not a Wieferich prime.