R. Bastos

most citedFiniteness conditions for the weak commutativity construction

1 citations · 1 across the 1 of their papers we have counts for

collaborators

7 papers

math.GR2019

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★ 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.GR2018

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

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

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

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 $ω (G)$ .…