Starting with an integral domain D of characteristic 0, we consider a class of iterated wreath product \(W_n\) of n copies of D. In order that \(W_n\) be transfinite hypercentral, it is necessary to restrict to the case of wreath products defined by way of numerical polynomials. We also associate to each of these groups a Lie ring, providing a correspondence preserving most of the structure. This construction generalizes a result of Sushchansky and Netreba (Algebra Discrete Math 122–132, 2005) which characterizes the Lie algebras associated to the Sylow \(p\) -subgroups of the symmetric group \({{\,\textrm{Sym}\,}}(p^n)\) . As an application, we explore the normalizer chain \(\lbrace \textbf{N}_{i}\rbrace _{i\ge -1}\) starting from the canonical regular abelian subgroup T of \(W_n\) . Finally, we characterize the regular abelian normal subgroups of \(\textbf{N}_0\) that are isomorphic to \(D^n\) .
