7 citations · 25 across the 12 of their papers we have counts for
15 papers
On the Self-Similarity of Permutational Wreath Products and Their Embedding into Finitely Presented Simple Groups
Mailton Rego Almeida, Alex Carrazedo Dantas, Altair Santos de Oliveira-Tosti
In this work, we study the self-similarity of permutational wreath products of the form \(A \wr_X G\), where \(A\) is a finitely generated abelian group and \(G\) is a self-similar…
Some families of locally graded groups with finitely many orbits under automorphisms
Alex Carrazedo Dantas, Jucélia Ferreira de Sousa
In this work, we study three families of locally graded groups with finitely many orbits under automorphisms. We prove that: (i) a residually finite group with finitely many orbits…
On a Class of Self-Similar Polycyclic Groups
A. C. Dantas, E. de Melo, R. N. de Oliveira +1
A group is self-similar if it admits a triple where is a subgroup of and a simple homomorphism, that is, the only subgroup of , normal in…
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…
On wreath product occurring as subgroup of automata group
Alex C. Dantas, Junio R. Oliveira, Tulio M. G. Santos
A finitely generated group is said to be an automata group if it admits a faithful self-similar finite-state representation on some regular -tree. We prove that if is a subg…
Self-similar abelian groups and their centralizers
Alex C. Dantas, Tulio M. G. Santos, Said N. Sidki
We extend results on transitive self-similar abelian subgroups of the group of automorphisms of an -ary tree in \cite{BS}, to the general case wh…