The LERF conjecture for groups with Kazhdan property (T)

Let $G$ be a countable group with Kazhdan property (T). LERF conjecture. The group $G$ is LERF if and only if it is finite.

The preceding proposition establishes the corresponding equivalence between A-separability and LERF for property (T) groups. The conjecture asserts that no infinite countable property (T) group is LERF, extending the obstruction discussed for higher-rank lattices; its status is not resolved in the source.