This analysis demonstrates subgroup separability in central extensions of hyperbolic groups, indicating key relationships with double coset separability.
We show that a central extension of locally quasiconvex subgroup separable hyperbolic group is product separable, so long as it is subgroup separable. We also establish that a central extension of a double coset separable group by a finitely generated group is double coset separable if and only if it is subgroup separable, and that double coset separability is stable under taking direct products with finitely generated nilpotent groups.
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Lawk Mineh (2025) studied this question.
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