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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(k) 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
References
Publication
Received: 29 August 2018
Revised: 28 November 2018
Accepted: 11 May 2019
Published: 17 December 2019
Authors
Rita Gitik
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States