Acylindrically hyperbolic groups with exotic properties

JOURNAL OF ALGEBRA

卷:522

Article

Minasyan, Ashot¹  Osin, Denis² 

[1] Univ Southampton, Math Sci, Southampton SO17 1BJ, Hants, England

[2] Vanderbilt Univ, Dept Math, 1326 Stevenson Ctr, Nashville, TN 37240 USA

关键词: Acylindrically hyperbolic groups;    Fixed point properties;   

DOI  :  10.1016/j.jalgebra.2018.12.011

来源: Elsevier

【 摘 要 】

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 FLP for all p is an element of [1, +infinity), 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 behavior. E.g., Q is not uniformly non-amenable and has finite generating sets with arbitrary large balls consisting of torsion elements. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free