JournalsggdVol. 5, No. 2pp. 213–230

The rank gradient from a combinatorial viewpoint

  • Miklós Abért

    Hungarian Academy of Sciences, Budapest, Hungary
  • Andrei Jaikin-Zapirain

    Universidad Autónoma de Madrid, Spain
  • Nikolay Nikolov

    University of Oxford, UK
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Abstract

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.

Cite this article

Miklós Abért, Andrei Jaikin-Zapirain, Nikolay Nikolov, The rank gradient from a combinatorial viewpoint. Groups Geom. Dyn. 5 (2011), no. 2, pp. 213–230

DOI 10.4171/GGD/124