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


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