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

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 $C^{\ast }$-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.

30 pages

References in corpus (1)

• C*-simplicity of free products with amalgamation and radical classes of groups

Cited by in corpus (1)

• A characterization of high transitivity for groups acting on trees