A. Miasnikov

collaborators

5 papers

math.GR2026

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 $Z^{m} wr Z^{n}$ , where $m, n \in N$ , are regularly bi-interpretable with $Z$ and therefore are first-order ri…

math.GR2026

Tensor completions of 2-nilpotent finitely generated torsion-free groups

Mikheil Amaglobeli, Alexei Miasnikov

In this paper, we study tensor completions $G \otimes_{N_{2, R}} R$ of finitely generated torsion-free nilpotent groups $G$ of class $2$ in the quasivariety $\mathcal{N}_{…

math.GR2025

First-order sentences in random groups III

Olga Kharlampovich, Alexei Miasnikov, Rizos Sklinos

We show that a first-order sentence is almost surely true in a random group of density d<1/2 if and only if it is true in a non-abelian free group.

math.GR2025

Groups elementary equivalent to finitely generated free metabelian

Olga Kharlampovich, Alexei Miasnikov

We describe groups elementarily equivalent to a free metabelian group with n generators. We also explore an exponentiation that naturally occurs in metabelian groups.

math.GR2025

The Diophantine problem in iterated wreath products of free abelian groups is undecidable

Olga Kharlampovich, Alexei Miasnikov

In this paper we prove that the Diophantine problem in iterated restricted wreath products $G$ of arbitrary non-trivial free abelian groups $A_{1}, \dots, A_{k}$ , $k > 1$ of finite ranks…