We show that Out(G) is residually finite if G is one-ended and hyperbolic relative to virtually polycyclic subgroups. More generally, if G is one-ended and hyperbolic relative to proper residually finite subgroups, the group of outer automorphisms preserving the peripheral structure is residually finite. We also show that Out(G) is virtually residually p-finite for every prime p if G is one-ended and toral relatively hyperbolic, or infinitely-ended and virtually residually p-finite.
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