Realising wreath products of cyclic groups as Galois groups

Abstract

Let K be any field of characteristic 0 and let T and X be algebraically independent over K . For n ≥ 1 let k ( n ) ≥ 2 be an integer and let fn ( X , T ) = x k(n) + T e K [ X , T ]. We shall regard T as a “parameter” and X as a “variable”. We put F 1 ( X , T ) = f 1 ( X , T ) and define, for n ≥ 1,