3 papers
math.GR2025
On self-similarity of finitely generated torsion-free nilpotent groups
Adilson Berlatto, Tulio Santos
This paper aims to investigate the self-similarity property in finitely-generated torsion-free nilpotent groups. We establish connections between geometric equivalence and self-sim…
math.GR2024
Self-similarity of some soluble relatively free groups
Adilson A. Berlatto, Alex C. Dantas, Tulio M. G. Santos
In this paper we prove that a free nilpotent group of finite rank is transitive self-similar. In contrast, we prove that a free metabelian group of rank is not transitiv…
math.GR2006
Virtual Endomorphisms of Nilpotent Groups
Adilson Berlatto, Said Sidki
A virtual endomorphism of a group G is a homomorphism f from H into G where H is a subgroup of G of finite index m. The triple (G,H,f) produces a state-closed (or, self-similar) re…