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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.

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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