Algebraic subgroups of acylindrically hyperbolic groups

JOURNAL OF ALGEBRA

卷:476

Article

Jacobson, B.¹ 

[1] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

关键词: Equations over groups;    Acylindrically hyperbolic groups;    Geometric group theory;   

DOI  :  10.1016/j.jalgebra.2016.11.029

来源: Elsevier

【 摘 要 】

A subgroup of a group G is called algebraic if it can be expressed as a finite union of solution sets to systems of equations. We prove that a non-elementary subgroup H of an acylindrically hyperbolic group G is algebraic if and only if there exists a finite subgroup K of G such that C-G(K) <= H <= N-G(K). We provide some applications of this result to free products, torsion-free relatively hyperbolic groups, and ascending chains of algebraic subgroups in acylindrically hyperbolic groups. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free