Título:	On profinite groups with automorphisms whose fixed points have countable Engel sinks
Autor(es):	Khukhro, Evgeny I. Shumyatsky, Pavel
Assunto:	Grupos profinitos Automorfismos Grupo Engel
Data de publicação:	24-Dez-2021
Editora:	Springer
Referência:	KHUKHRO, Evgeny I.; SHUMYATSKY, Pavel. On profinite groups with automorphisms whose fixed points have countable Engel sinks. IIsrael Journal of Mathematics, [S.l.], 2021. DOI: https://doi.org/10.1007/s11856-021-2267-1.
Abstract:	An Engel sink of an element g of a group G is a set E(g) such that for every x ∈ G all sufficiently long commutators [⋯[[x, g], g],…, g] belong to E(g). (Thus, g is an Engel element precisely when we can choose E(g)={1}.) It is proved that if a profinite group G admits an elementary abelian group of automorphisms A of coprime order q2 for a prime q such that for each a ∈ A {1} every element of the centralizer CG(a) has a countable (or finite) Engel sink, then G has a finite normal subgroup N such that G/N is locally nilpotent.
DOI:	https://doi.org/10.1007/s11856-021-2267-1
Versão da editora:	https://link.springer.com/article/10.1007/s11856-021-2267-1
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