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arXiv · 1305.5403

Residual properties of automorphism groups of (relatively) hyperbolic groups

Gilbert Levitt·Ashot Minasyan
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Abstract

We show that Out(G) is residually finite if G is a one-ended group that is 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 p-residually finite for every prime p if G is one-ended and toral relatively hyperbolic, or infinitely-ended and virtually p-residually finite.

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Gilbert Levitt, Ashot Minasyan. 2013-05-23. Residual properties of automorphism groups of (relatively) hyperbolic groups. https://doi.org/10.2140/gt.2014.18.2985

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