Strong accessibility for finitely presented groups
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 hyperbolic groups which are (virtually) without $2$torsion and finitely presented subgroups of SL(n,Z) are both finite.
 Publication:

arXiv eprints
 Pub Date:
 February 2013
 arXiv:
 arXiv:1302.5451
 Bibcode:
 2013arXiv1302.5451L
 Keywords:

 Mathematics  Group Theory
 EPrint:
 29 pages, 11 figures. author note: the arXiv admin note refers to a quotation. arXiv admin note: text overlap with arXiv:math/0507424 by other authors