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Separability of Subsets in Infinite Groups
We study the separability of subsets of an infinite group. Given an infinite group $G$ and subsets $A,B\subset G$, we say that $A$ and $B$ are separated in $G$ if there exists an infinite symmetric subset $X\subset G$ with $e\in X$ and $XAX\cap B=\varnothing$. Question 17.102 of the Kourovka Noteboo
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