#### Volume 19, issue 7 (2019)

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On local tameness of certain graphs of groups

### Rita Gitik

Algebraic & Geometric Topology 19 (2019) 3701–3710
##### Abstract

Let $G$ be the fundamental group of a finite graph of groups with Noetherian edge groups and locally tame vertex groups. We prove that $G$ is locally tame. It follows that if a finitely presented group $H$ has a nontrivial $JSJ$–decomposition over the class of its $VPC\left(k\right)$ subgroups for $k=1$ or $k=2$, and all the vertex groups in the decomposition are flexible, then $H$ is locally tame.

##### Keywords
Noetherian group, locally tame group, graph of groups, \JSJ–decomposition, covering space, fundamental group
##### Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 20E06, 20F34, 57M07, 57M10