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Compact groups in which all elements have countable right Engel sinks
Published online by Cambridge University Press: 13 November 2020
Abstract
A right Engel sink of an element g of a group G is a set ${\mathscr R}(g)$ such that for every x ∈ G all sufficiently long commutators $[...[[g,x],x],\dots ,x]$ belong to ${\mathscr R}(g)$. (Thus, g is a right Engel element precisely when we can choose ${\mathscr R}(g)=\{ 1\}$.) It is proved that if every element of a compact (Hausdorff) group G has a countable right Engel sink, then G has a finite normal subgroup N such that G/N is locally nilpotent.
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- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 6 , December 2021 , pp. 1790 - 1814
- Copyright
- Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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