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Dec 28, 2019 at 16:46 comment added HJRW @YanivShakhar: They're linear, and hence virtually torsion free. Probably there are explicit examples of quaterionionic hyperbolic lattices with torsion, but if you want to construct a hyperbolic group with torsion and property (T), just take any non-trivial element $g$ and kill a sufficiently high power $g^n$.
Dec 27, 2019 at 15:13 vote accept Yaniv Shakhar
Dec 27, 2019 at 12:12 comment added AGenevois I am not quite familiar with lattices in quaternionic hyperbolic spaces, but there are reflections in such spaces, so I would say that there exist torsion-free lattices and lattices with torsion.
Dec 27, 2019 at 11:22 comment added Yaniv Shakhar Do you know if uniform lattices in quaternionic hyperbolic spaces have torsion or are torsion free?
Dec 26, 2019 at 11:06 history answered AGenevois CC BY-SA 4.0