Algebraic subgroups of acylindrically hyperbolic groups

作者：Jacobson B^*

来源：Journal of Algebra, 2017, 476: 113-133.

DOI：10.1016/j.jalgebra.2016.11.029

• Equations over groups
• Acylindrically hyperbolic groups
• Geometric group theory

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.

• 出版日期2017-4-15