Compact groups in which all elements have countable right Engel sinks

DOI10.1017/PRM.2020.81arXiv2004.11680MaRDI QIDQ6339360

Pavel Shumyatsky, Evgenii I. Khukhro

Publication date: 21 April 2020

Abstract: A right Engel sink of an element $g$ of a group $G$ is a set $mathscrR(g)$ such that for every $xinG$ all sufficiently long commutators $[...[[g,x],x],dots,x]$ belong to $mathscrR(g)$. (Thus, $g$ is a right Engel element precisely when we can choose $mathscrR(g)=1$.) It is proved that if every element of a compact (Hausdorff) group $G$ has a countable (or finite) right Engel sink, then $G$ has a finite normal subgroup $N$ such that $G/N$ is locally nilpotent.

Mathematics Subject Classification ID

Generalizations of solvable and nilpotent groups (20F19) Compact groups (22C05) Engel conditions (20F45) Limits, profinite groups (20E18)

This page was built for publication: Compact groups in which all elements have countable right Engel sinks

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6339360)