Volume 21, issue 3 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 22, 1 issue

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Strong accessibility for finitely presented groups

Larsen Louder and Nicholas Touikan

Geometry & Topology 21 (2017) 1805–1835

A hierarchy of a group is a rooted tree of groups obtained by iteratively passing to vertex groups of graphs of groups decompositions. We define a (relative) slender JSJ hierarchy for (almost) finitely presented groups and show that it is finite, provided the group in question doesn’t contain any slender subgroups with infinite dihedral quotients and satisfies an ascending chain condition on certain chains of subgroups of edge groups.

As a corollary, slender JSJ hierarchies of finitely presented subgroups of SLn() or of hyperbolic groups which are (virtually) without 2–torsion are finite.

strong accessibility, graph of groups, hierarchy
Mathematical Subject Classification 2010
Primary: 20E08, 20F65, 20F67, 57M60
Received: 22 September 2015
Accepted: 5 April 2016
Published: 10 May 2017
Proposed: Benson Farb
Seconded: Dmitri Burago, Danny Calegari
Larsen Louder
Department of Mathematics
University College London
Gower Street
United Kingdom
Nicholas Touikan
Department of Mathematical Sciences
Stevens Institute of Technology
1 Castle Point on Hudson
Hoboken, NJ 07030
United States