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.

中文翻译：

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所有元素都有可数右恩格尔汇的紧群

元素的右恩格尔汇G一组的G是一个集合${\mathscr R}(g)$这样对于每个X∈G所有足够长的换向器$[...[[g,x],x],\dots ,x]$属于${\mathscr R}(g)$. （因此，G正是当我们可以选择时，它是一个正确的恩格尔元素${\mathscr R}(g)=\{ 1\}$.) 证明了如果紧（Hausdorff）群的每一个元素G有一个可数右恩格尔槽，则G有一个有限正规子群ñ这样G/ñ是局部幂零的。