23 citations · 47 across the 20 of their papers we have counts for
19 papers · 1 filter
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 , where , are regularly bi-interpretable with and therefore are first-order ri…
Tensor completions of 2-nilpotent finitely generated torsion-free groups
Mikheil Amaglobeli, Alexei Miasnikov
In this paper, we study tensor completions of finitely generated torsion-free nilpotent groups of class in the quasivariety $\mathcal{N}_{…
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.
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 of arbitrary non-trivial free abelian groups , of finite ranks…
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.
Metabelian groups: full-rank presentations, randomness and Diophantine problems
Albert Garreta, Leire Legarreta, Alexei Miasnikov +1
We study metabelian groups given by full rank finite presentations in the variety of metabelian groups. We prove that …