Normal automorphisms of relatively hyperbolic groups

By Ashot Minasyan, Denis V. Osin. 2008

50 citations recorded by the source corpus.

An automorphism of a group G is normal if it fixes every normal subgroup of G setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively hyperbolic group G, Inn(G) has finite index in the subgroup Aut_n(G) of normal automorphisms. If, in addition, G is non-elementary and has no non-trivial finite normal subgroups, then Aut_n(G)=Inn(G). As an application, we show that Out(G) is residually finite for every finitely generated residually finite group G with more than one end.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e0a2c68b462bc0d70474d0938f1bcfbd098a114b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Denis V. Osin

In Discrete Mathematics and Combinatorics

1. Denis V. Osin
2. Michael Hull
3. Alessandro Sisto
4. Yves Cornulier

In Geometry and Topology

1. Denis V. Osin
2. Alessandro Sisto
3. Ashot Minasyan
4. Michael Hull
5. Anthony Genevois
6. Jason A. Behrstock
7. Mark F. Hagen
8. D. Groves

Citations in the corpus

• Acylindrically hyperbolic groups (2013, result): “Their results are similar to the classification obtained in [37] for relatively hyperbolic groups.”
• Acylindrical hyperbolicity of groups acting on trees (2013, unknown): “The proof is based on the approach suggested in [63] and essentially uses acylindrical hyperbolicity.”
• GROUPS ACTING ACYLINDRICALLY ON HYPERBOLIC SPACES (2017, background): “This result opens the door for Monod and Shalom [2006] rigidity theory for group actions on spaces with measure.”