Danilo Silveira

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20182020

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5 papers · 1 filter

math.GR2020

On residually finite groups satisfying an Engel type identity

Danilo Silveira

Let $n, q$ be positive integers. We show that if $G$ is a finitely generated residually finite group satisfying the identity $[x,_{n} y^{q}] \equiv 1,$ then there exists a function…

math.GR2019

Engel-like conditions in fixed points of automorphisms of profinite groups

Cristina Acciarri, Danilo Silveira

Let $q$ be a prime and $A$ an elementary abelian $q$ -group acting as a coprime group of automorphisms on a profinite group $G$ . We show that if $A$ is of order $q^{2}$ and some power…

math.GR2019

On finite groups in which commutators are covered by Engel subgroups

Pavel Shumyatsky, Danilo Silveira

Let $m, n$ be positive integers and $w$ a multilinear commutator word. Assume that $G$ is a finite group having subgroups $G_{1}, \dots, G_{m}$ whose union contains all $w$ -values in $G$ …

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

Engel sinks of fixed points in finite groups

Cristina Acciarri, Pavel Shumyatsky, Danilo Sanção da Silveira

For an element $g$ of a group $G$ , an Engel sink is a subset $E (g)$ such that for every $x \in G$ all sufficiently long commutators $[x, g, g, \dots, g]$ belong to $\math…