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Compact groups in which all elements have countable right Engel sinks
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 151 / Issue 6 / December 2021
- Published online by Cambridge University Press:
- 13 November 2020, pp. 1790-1814
- Print publication:
- December 2021
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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.
Linear Groups with Almost Right Engel Elements
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 62 / Issue 3 / August 2019
- Published online by Cambridge University Press:
- 30 January 2019, pp. 789-797
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Let G be a linear group such that for every g ∈ G there is a finite set
${\cal R}(g)$ with the property that for every x ∈ G all sufficiently long commutators [g, x, x, …, x] belong to 
${\cal R}(g)$. We prove that G is finite-by-hypercentral.
Torsion-free groups isomorphic to all of their non-nilpotent subgroups
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- Journal:
- Journal of the Australian Mathematical Society / Volume 71 / Issue 3 / December 2001
- Published online by Cambridge University Press:
- 09 April 2009, pp. 339-348
- Print publication:
- December 2001
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