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- W2970248880 abstract "An Engel sink of an element $g$ of a group $G$ is a set ${mathscr E}(g)$ such that for every $xin G$ all sufficiently long commutators $[...[[x,g],g],dots ,g]$ belong to ${mathscr E}(g)$. (Thus, $g$ is an Engel element precisely when we can choose ${mathscr E}(g)={ 1}$.) It is proved that if every element of a compact (Hausdorff) group $G$ has a countable (or finite) Engel sink, then $G$ has a finite normal subgroup $N$ such that $G/N$ is locally nilpotent. This settles a question suggested by J. S. Wilson." @default.
- W2970248880 created "2019-09-05" @default.
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- W2970248880 date "2019-08-30" @default.
- W2970248880 modified "2023-10-18" @default.
- W2970248880 title "Compact groups with countable Engel sinks" @default.
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- W2970248880 doi "https://doi.org/10.48550/arxiv.1908.11637" @default.
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