Groups, Geometry, and Dynamics

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Volume 5, Issue 2, 2011, pp. 213–230
DOI: 10.4171/GGD/124

Published online: 2011-03-06

The rank gradient from a combinatorial viewpoint

Miklós Abért[1], Andrei Jaikin-Zapirain[2] and Nikolay Nikolov[3]

(1) Hungarian Academy of Sciences, Budapest, Hungary
(2) Universidad Autónoma de Madrid, Spain
(3) University of Oxford, UK

This paper investigates the asymptotic behaviour of the minimal number of generators of finite index subgroups in residually finite groups. We analyze three natural classes of groups: amenable groups, groups possessing an infinite soluble normal subgroup and virtually free groups. As a tool for the amenable case we generalize Lackenby's trichotomy theorem on finitely presented groups.

Keywords: Rank gradient, amalgam, amenable group, Lück approximation

Abért Miklós, Jaikin-Zapirain Andrei, Nikolov Nikolay: The rank gradient from a combinatorial viewpoint. Groups Geom. Dyn. 5 (2011), 213-230. doi: 10.4171/GGD/124