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 2018Show all

6 papers · 1 filter

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…