Expanders, rank and graphs of groups

dc.creatorLackenby, Marc
dc.date2004-03-08
dc.date2005-04-01
dc.date.accessioned2026-07-07T05:06:11Z
dc.date.available2026-07-07T05:06:11Z
dc.descriptionLet G be a finitely presented group, and let {G_i} be a collection of finite index normal subgroups that is closed under intersections. Then, we prove that at least one of the following must hold: 1. G_i is an amalgamated free product or HNN extension, for infinitely many i; 2. the Cayley graphs of G/G_i (with respect to a fixed finite set of generators for G) form an expanding family; 3. inf_i (d(G_i)-1)/[G:G_i] = 0, where d(G_i) is the rank of G_i. The proof involves an analysis of the geometry and topology of finite Cayley graphs. Several applications of this result are given.
dc.description13 pages; to appear in Israel J. Math
dc.identifierhttps://arxiv.org/abs/math/0403127
dc.identifierhttp://arxiv.org/abs/math/0403127
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70383
dc.subjectGroup Theory
dc.subjectGeometric Topology
dc.subject20F65; 20E06, 20F05, 05C25
dc.titleExpanders, rank and graphs of groups
dc.typetext

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