Disjoint subsets of cardinality smaller than an infinite group need not be separable, refuting Problem 17.102.
Newelski,On the number of squares in a group, Proc
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Counterexamples to Problem 17.102 of the Kourovka Notebook: Negation and Discussion of Separability Conditions in Infinite Groups
Disjoint subsets of cardinality smaller than an infinite group need not be separable, refuting Problem 17.102.