Geodesic
The rank gradient from a combinatorial viewpoint
Miklós Abért1 orcid ; Andrei Jaikin-Zapirain2 orcid ; Nikolay Nikolov3
1Hungarian Academy of Sciences, Budapest, Hungary
2Universidad Autónoma de Madrid, Spain
3University of Oxford, UK
Groups, geometry, and dynamics, Tome 5 (2011) no. 2, pp. 213-230

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DOI

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.
DOI : 10.4171/ggd/124
Classification : 20-XX, 00-XX
Mots-clés : Rank gradient, amalgam, amenable group, Lück approximation

Miklós Abért  1   ; Andrei Jaikin-Zapirain  2   ; Nikolay Nikolov  3

1 Hungarian Academy of Sciences, Budapest, Hungary
2 Universidad Autónoma de Madrid, Spain
3 University of Oxford, UK 
Miklós Abért; Andrei Jaikin-Zapirain; Nikolay Nikolov. The rank gradient from a combinatorial viewpoint. Groups, geometry, and dynamics, Tome 5 (2011) no. 2, pp. 213-230. doi: 10.4171/ggd/124
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