7 papers
Equations in Products of Free Groups and 3-Manifold Groups II: Olshanskii Epimorphisms
Olga Kharlampovich, Alina Vdovina
In 1989 Olshanskii introduced a three-parameter family of coordinate-surjective homomorphisms from the genus-two surface group to a direct product of two rank-two free groups. When…
Equations in Products of Free Groups and 3-Manifold Groups, I
Olga Kharlampovich, Alina Vdovina
Perelman's proof of the Poincare conjecture shows that every simply connected closed 3-manifold is homeomorphic to the 3-sphere. The fundamental groups of 3-manifolds attract lots…
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…
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.
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.
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…