Erratum to the paper "Acylindrical hyperbolicity of groups acting on trees"

TL;DR

This paper corrects a gap in previous work on the invariance of acylindrical hyperbolicity of groups under commensurability, clarifying the conditions and proofs involved.

Contribution

It identifies and rectifies a proof gap in earlier results regarding acylindrical hyperbolicity invariance under commensurability.

Findings

Correction of the proof gap in previous theorems

Updated statements and proofs in related papers

Clarification of conditions for acylindrical hyperbolicity invariance

Abstract

In our paper arXiv:1310.6289, we stated that acylindrical hyperbolicity of a group is invariant under commensurability up to finite kernels. Unfortunately, the proof of this fact contained a gap. The goal of this erratum is to point out the gap and to correct the statements and proofs of results of arXiv:1310.6289 and the subsequent paper arXiv:1501.03066 affected by it.