4 papers · 1 filter
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…