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Small cancellation and
outer automorphisms of Kazhdan groups acting on hyperbolic
spaces
Ionuţ Chifan, Adrian Ioana, Denis Osin and Bin Sun |
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Algebraic & Geometric Topology 25 (2025) 5463–5501
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Abstract |
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We show that every finite group is realized as the outer automorphism group of a hyperbolic group with Kazhdan property (T) and trivial finite radical. This result complements the well-known theorem of Paulin stating that the outer automorphism group of every hyperbolic group with property (T) is finite. We also show that, for every countable group , there exists an acylindrically hyperbolic group with property (T) such that . The proofs employ strengthened versions of some previously known results in small cancellation theory. |
Keywords
Kazhdan's property (T), outer automorphism, small
cancellation, hyperbolic groups, acylindrically hyperbolic
groups
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Mathematical Subject Classification
Primary: 20F65
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References |
Publication
Received: 14 April 2023
Revised: 6 April 2024
Accepted: 24 June 2024
Published: 18 December 2025
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Authors |
| Ionuţ Chifan | |
| Department of Mathematics The University of Iowa Iowa City, IA United States |
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| Adrian Ioana | |
| Department of Mathematics University of California San Diego La Jolla, CA United States |
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| Denis Osin | |
| Mathematics Department Vanderbilt University Nashville, TN United States |
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| Bin Sun | |
| Michigan State University East Lansing, MI United States |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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