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Acylindrically hyperbolic groups with exotic properties

Acylindrically hyperbolic groups with exotic properties
Acylindrically hyperbolic groups with exotic properties
We prove that every countable family of countable acylindrically hyperbolic groups has a common finitely generated acylindrically hyperbolic quotient. As an application, we obtain an acylindrically hyperbolic group Q with strong fixed point properties: Q has property FL^p for all p∈[1,+∞),and every action of Q on a finite dimensional contractible topological space has a fixed point. In addition, Q has other properties which are rather unusual for groups exhibiting "hyperbolic-like" behaviour. E.g., Q is not uniformly non-amenable and has finite generating sets with arbitrary large balls consisting of torsion elements.
0021-8693
218-235
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Osin, Denis
32a9932c-f439-4b83-b639-1a53ac6bf6f5
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Osin, Denis
32a9932c-f439-4b83-b639-1a53ac6bf6f5

Minasyan, Ashot and Osin, Denis (2019) Acylindrically hyperbolic groups with exotic properties. Journal of Algebra, 522, 218-235. (doi:10.1016/j.jalgebra.2018.12.011).

Record type: Article

Abstract

We prove that every countable family of countable acylindrically hyperbolic groups has a common finitely generated acylindrically hyperbolic quotient. As an application, we obtain an acylindrically hyperbolic group Q with strong fixed point properties: Q has property FL^p for all p∈[1,+∞),and every action of Q on a finite dimensional contractible topological space has a fixed point. In addition, Q has other properties which are rather unusual for groups exhibiting "hyperbolic-like" behaviour. E.g., Q is not uniformly non-amenable and has finite generating sets with arbitrary large balls consisting of torsion elements.

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Accepted/In Press date: 28 December 2018
e-pub ahead of print date: 2 January 2019
Published date: 15 March 2019

Identifiers

Local EPrints ID: 427350
URI: http://eprints.soton.ac.uk/id/eprint/427350
DOI: doi:10.1016/j.jalgebra.2018.12.011
ISSN: 0021-8693
PURE UUID: ff9c52fc-28b5-47ac-824d-c190fa0adcf7
ORCID for Ashot Minasyan: ORCID iD orcid.org/0000-0002-4986-2352

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Date deposited: 14 Jan 2019 17:30
Last modified: 16 Mar 2024 07:28

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Author: Ashot Minasyan ORCID iD
Author: Denis Osin

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