On the first-order genus of wreath products and their central extensions

Olga Kharlampovich, Alexei Miasnikov, Denis Osin

We prove that groups of the form ${\mathbb{Z}}^m\mathrm{wr}{\mathbb{Z}}^n$, where $m,n\in \mathbb{N}$, are regularly bi-interpretable with $\mathbb{Z}$ and therefore are first-order ri…