Geometry & Topology

Strong accessibility for finitely presented groups

Larsen Louder and Nicholas Touikan

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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.

Article information

Geom. Topol., Volume 21, Number 3 (2017), 1805-1835.

Received: 22 September 2015
Accepted: 5 April 2016
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20E08: Groups acting on trees [See also 20F65] 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F67: Hyperbolic groups and nonpositively curved groups 57M60: Group actions in low dimensions

strong accessibility graph of groups hierarchy


Louder, Larsen; Touikan, Nicholas. Strong accessibility for finitely presented groups. Geom. Topol. 21 (2017), no. 3, 1805--1835. doi:10.2140/gt.2017.21.1805.

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