Algebraic subgroups of acylindrically hyperbolic groups

2015/11/26 by Jacobson, Bryan · 2 citations
#20F65 #20F67 #20F70 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1511.08297

Abstract

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.

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• Boundary dynamics, triple transitivity, and mixed identities in weakly hyperbolic groups
• A note on intrinsic topologies of groups

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