A. Miasnikov

activity

20062026

most citedStallings graphs for quasi-convex subgroups

23 citations · 47 across the 20 of their papers we have counts for

collaborators

24 papers

math.AG2026

An explicit tame factorization of the four-variable Anick automorphism

Alexei Miasnikov, Ivan Shestakov

Let $δ = x z - y t$ . We give an explicit tame factorization of the Anick automorphism $(x + δ t, y + δ z, z, t)$ of $F [x, y, z, t]$ . After a linear change of coordinates, the factorization consists…

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

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…

math.GR2023

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.