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

26 papers

math.GR2024

Generalized torsion elements in infinite groups

Raimundo Bastos, Luis Mendonça

A group element is called generalized torsion if a finite product of its conjugates is equal to the identity. We show that in a finitely generated abelian-by-finite group, an eleme…

math.GR2023★ 2 cited

Generalized torsion elements in groups

Raimundo Bastos, Csaba Schneider, Danilo Silveira

A group element is called a generalized torsion if a finite product of its conjugates is equal to the identity. We prove that in a nilpotent or FC-group, the generalized torsion el…

math.GR2020★ 1 cited

Virtually nilpotent groups with finitely many orbits under automorphisms

Raimundo Bastos, Alex C. Dantas, Emerson de Melo

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

math.GR2020

Groups with a solvable subgroup of prime-power index

Raimundo Bastos, Csaba Schneider

In this paper we describe some properties of groups $G$ that contain a solvable subgroup of finite prime-power index (Theorem 1 and Corollaries 2--3). We prove that if $G$ is a non…

math.GR2019★ 2 cited

Soluble Groups with few orbits under automorphisms

Raimundo Bastos, Alex Carrazedo Dantas, Emerson de Melo

Let $G$ be a group. The orbits of the natural action of Aut $(G)$ on $G$ are called ``automorphism orbits'' of $G$ , and the number of automorphism orbits of $G$ is denoted by $ω (G)$ …

math.GR2019

Boundedly finite conjugacy classes of tensors

Raimundo Bastos, Carmine Monetta

Let $n$ be a positive integer and let $G$ be a group. We denote by $ν (G)$ a certain extension of the non-abelian tensor square $G \otimes G$ by $G \times G$ . Set $T_{\otimes}(G) =…

math.GR2019★ 1 cited

Finiteness conditions for the weak commutativity construction

Raimundo Bastos, Bruno Lima, Ricardo Nunes

The operator, $χ$ , of weak commutativity between isomorphic groups $G$ and $G^{φ}$ was introduced by Sidki as \begin{equation*} χ(G)=\left\langle G \cup G^{φ}\mid \lbrack g,g^{φ}]=…

math.GR2019★ 7 cited

Non-abelian tensor square and related constructions of $p$ -groups

Raimundo Bastos, Emerson de Melo, Nathália Gonçalves +1

Let $G$ be a group. We denote by $ν (G)$ a certain extension of the non-abelian tensor square $[G, G^{φ}]$ by $G \times G$ . We prove that if $G$ is a finite potent $p$ -group, then $[G,…

math.GR2018★ 3 cited

Finiteness of homotopy groups related to the non-abelian tensor product

Raimundo Bastos, Noraí R. Rocco, Ewerton R. Vieira

By using finiteness related result of non-abelian tensor product we prove finiteness conditions for the homotopy groups $π_{n} (X)$ in terms of the number of tensors. In particular, w…

math.GR2018★ 1 cited

The order of the non-abelian tensor product of groups

Raimundo Bastos, Irene N. Nakaoka, Noraí R. Rocco

Let $G$ and $H$ be groups that act compatibly on each other. We denote by $[G, H]$ the derivative subgroup of $G$ under $H$ . We prove that if the set $\{g^{-1}g^h \mid g \in G, h \i…

math.GR2018★ 1 cited

Bounded Engel elements in residually finite groups

Raimundo Bastos, Danilo Silveira

Let $q$ be a prime. Let $G$ be a residually finite group satisfying an identity. Suppose that for every $x \in G$ there exists a $q$ -power $m = m (x)$ such that the element $x^{m}$ is a…

math.GR2018★ 6 cited

Coprime commutators in finite groups

Carmine Monetta, Raimundo Bastos

Let $G$ be a finite group and let $k \geq 2$ . We prove that the coprime subgroup $γ_{k}^{*} (G)$ is nilpotent if and only if $∣ x y ∣ = ∣ x ∣∣ y ∣$ for any $γ_{k}^{*}$ -commutators $x, y \in G$ of cop…

math.GR2018★ 4 cited

FC-groups with finitely many automorphism orbits

Raimundo A. Bastos, Alex C. Dantas

Let $G$ be a group. The orbits of the natural action of $A u t (G)$ on $G$ are called "automorphism orbits" of $G$ , and the number of automorphism orbits of $G$ is denoted by $ω (G)$ .…

math.GR2018★ 4 cited

Maximal covers of finite groups

Igor Lima, Raimundo Bastos, José R. Rogério

Let $λ (G)$ be the maximum number of subgroups in an irredundant covering of the finite group $G$ . We prove that if $G$ is a group with $λ (G) ⩽ 6$ , then $G$ is supersolvable…

math.GR2017★ 3 cited

Non-abelian tensor product of residually finite groups

Raimundo Bastos, Noraí R. Rocco

Let $G$ and $H$ be groups that act compatibly on each other. We denote by $η (G, H)$ a certain extension of the non-abelian tensor product $G \otimes H$ by $G \times H$ . Suppose that…

math.GR2017★ 11 cited

A criterion for metanilpotency of a finite group

Raimundo Bastos, Carmine Monetta, Pavel Shumyatsky

We prove that the $k$ th term of the lower central series of a finite group $G$ is nilpotent if and only if $∣ ab ∣ = ∣ a ∣∣ b ∣$ for any $γ_{k}$ -commutators $a, b \in G$ of coprime orders.

math.GR2016★ 7 cited

Finiteness conditions for the non-abelian tensor product of groups

Raimundo Bastos, Irene N. Nakaoka, Noraí R. Rocco

Let $G$ , $H$ be groups. We denote by $η (G, H)$ a certain extension of the non-abelian tensor product $G \otimes H$ by $G \times H$ . We prove that if $G$ and $H$ are groups that act…

math.GR2016★ 14 cited

A Sufficient Condition for Nilpotency of the Commutator Subgroup

Raimundo Bastos, Pavel Shumyatsky

Let $G$ be a finite group with the property that if $a, b$ are commutators of coprime orders, then $∣ ab ∣ = ∣ a ∣∣ b ∣$ . We show that $G^{'}$ is nilpotent.

math.GR2016

A note on finiteness conditions for the non-abelian tensor square of groups

Raimundo Bastos, Noraí Romeu Rocco

Let $G$ be a group. We denote by $ν (G)$ a certain extension of the non-abelian tensor square $G \otimes G$ by $G \times G$ . We prove that if $G$ is a finitely generated group in wh…

math.GR2016★ 3 cited

The non-abelian tensor square of residually finite groups

Raimundo Bastos, Noraí Romeu Rocco

Let $m, n$ be positive integers and $p$ a prime. 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 a residuall…

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…