#### Volume 21, issue 3 (2017)

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Strong accessibility for finitely presented groups

### Larsen Louder and Nicholas Touikan

Geometry & Topology 21 (2017) 1805–1835
##### Abstract

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 ${SL}_{n}\left(ℤ\right)$ or of hyperbolic groups which are (virtually) without $2$–torsion are finite.

##### Keywords
strong accessibility, graph of groups, hierarchy
##### Mathematical Subject Classification 2010
Primary: 20E08, 20F65, 20F67, 57M60