R. Bastos

activity

20122024

most citedOn groups admitting a word whose values are Engel

17 citations · 115 across the 25 of their papers we have counts for

collaborators

Showing 2015Show all

5 papers · 1 filter

math.GR2015★ 7 cited

Finite Groups with 6 or 7 Automorphism Orbits

Alex Carrazedo Dantas, Martino Garonzi, Raimundo Bastos

Let $G$ be a group. The orbits of the natural action of $\mbox{Aut}(G)$ on $G$ are called "automorphism orbits" of $G$ , and the number of automorphism orbits of $G$ is denoted by $…

math.GR2015★ 4 cited

Non-abelian tensor square of finite-by-nilpotent groups

Raimundo Bastos, Norai R. Rocco

Let $G$ be a group. We denote by $ν (G)$ an extension of the non-abelian tensor square $G \otimes G$ by $G \times G$ . We prove that if $G$ is finite-by-nilpotent, then the non-abeli…

math.GR2015★ 6 cited

On finite groups with few automorphism orbits

Raimundo Bastos, Alex Carrazedo Dantas

Denote by $ω (G)$ the number of orbits of the action of $A u t (G)$ on the finite group $G$ . We prove that if $G$ is a finite nonsolvable group in which $ω (G) ⩽ 5$ , then $G$ is…

math.GR2015★ 3 cited

On residually finite groups with Engel-like conditions

Raimundo Bastos

Let $m, n$ be positive integers. Suppose that $G$ is a residually finite group in which for every element $x \in G$ there exists a positive integer $q = q (x) ⩽ m$ such that $x…

math.GR2015★ 8 cited

On profinite groups with Engel-like conditions

Raimundo Bastos, Pavel Shumyatsky

Let $G$ be a profinite group in which for every element $x \in G$ there exists a natural number $q = q (x)$ such that $x^{q}$ is Engel. We show that $G$ is locally virtually nilpotent. F…