Journal article
Small cancellation and outer automorphisms of Kazhdan groups acting on hyperbolic spaces
Algebraic & geometric topology, Vol.25(9), pp.5463-5501
12/18/2025
DOI: 10.2140/agt.2025.25.5463
Abstract
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 Q, there exists an acylindrically hyperbolic group G with property (T) such that Out(G)≅Q. The proofs employ strengthened versions of some previously known results in small cancellation theory.
Details
- Title: Subtitle
- Small cancellation and outer automorphisms of Kazhdan groups acting on hyperbolic spaces
- Creators
- Ionuţ Chifan - University of IowaAdrian Ioana - University of California San DiegoDenis Osin - Vanderbilt UniversityBin Sun - Michigan State University
- Resource Type
- Journal article
- Publication Details
- Algebraic & geometric topology, Vol.25(9), pp.5463-5501
- DOI
- 10.2140/agt.2025.25.5463
- ISSN
- 1472-2747
- eISSN
- 1472-2739
- Publisher
- MSP
- Number of pages
- 39
- Language
- English
- Date published
- 12/18/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9985114162102771
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