Stature and separability in graphs of groups

2019/04/12 by Jingyin Huang, Huang, Jingyin, Daniel T. Wise +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1904.06021

openalex publication_date 2019/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of finite stature of a family \H_i\ of subgroups of a group G. We investigate the separability of subgroups of a group G that splits as a graph of hyperbolic special groups with quasiconvex edge groups. We prove that when the vertex groups of G have finite stature, then quasiconvex subgroups of the vertex groups of G are separable in G. We present some partial results in a relatively hyperbolic framework.

Related

• Height in splittings of hyperbolic groups
• Deciding if a hyperbolic group splits over a given quasiconvex subgroup
• Decomposing groups by codimension-1 subgroups
• Quasiconvexity and relatively hyperbolic groups that split
• Strongly Quasiconvex subgroups in graphs of groups