We study the Diophantine problem (decidability of finite systems of equations) in different
classes of finitely generated solvable groups (nilpotent, polycyclic, metabelian, free solvable …

In this paper we show that the Diophantine problem in solvable Baumslag–Solitar groups $
BS (1, k) $ and in wreath products $ A\wr\mathbb {Z} $, where $ A $ is a finitely generated …

We introduce a model of random finitely generated, torsion-free, 2-step nilpotent groups (in
short, τ 2-groups). To do so, we show that these are precisely the groups with presentation of …

Recently, Macdonald et. al. showed that many algorithmic problems for finitely generated
nilpotent groups including computation of normal forms, the subgroup membership problem …

We solve Dehn's isomorphism problem for virtually torsion-free relatively hyperbolic groups
with nilpotent parabolic subgroups. We do so by reducing the isomorphism problem to three …

We consider two fields of study–random groups and cubulations–from their definitions and
history to current research. Motivated by group properties, we apply cubulation theory to a …

Random presentations and random subgroups: a survey arXiv:1702.01942v1 [math.GR] 7
Feb 2017 Page 1 Random presentations and random subgroups: a survey ∗ Frédérique …

In this paper we show that Diophantine problem in solvable Baumslag-Solitar groups BS (1,
k) is decidable, ie, there is an algorithm that given a finite system of equations with constants …

We first show that arithmetic is bi-interpretable (with parameters) with the free monoid and
with partially commutative monoids with trivial center. This bi-interpretability implies that …

We first show that arithmetic is bi-interpretable (with parameters) with the free monoid and
with partially commutative monoids with trivial center. This bi-interpretability implies that …