Two Families of Examples of Groups Acting on Trees with Nontrivial Quasi-Kernels

2020/03/23 by Nikolay A. Ivanov, Ivanov, Nikolay A.
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2003.10196

openalex publication_date 2020/03/23 · openalex created_date 2020/03/27 · openalex updated_date 2026/07/28

Abstract

We introduce two families of examples of groups acting on trees, one consisting of group amalgamations and the other consisting of HNN-extensions, motivated by the problems of C^*-simplicity and unique trace property. Moreover, we prove that our examples are not inner amenable and identify a relatively large, simple, normal subgroup in each one.

Related

• C*-simplicity of HNN extensions and groups acting on trees
• Characterising actions on trees yielding non-trivial quasimorphisms
• Groups acting on trees and the Eilenberg-Ganea problem for families
• Groups acting on trees with almost prescribed local action
• Quasi-actions on trees and Property (QFA)