- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:59
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
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5
2011
2
The rank gradient from a combinatorial viewpoint
Miklós
Abért
Hungarian Academy of Sciences, BUDAPEST, HUNGARY
Andrei
Jaikin-Zapirain
Universidad Autónoma de Madrid, MADRID, SPAIN
Nikolay
Nikolov
University of Oxford, OXFORD, UNITED KINGDOM
Rank gradient, amalgam, amenable group, Lück approximation
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.
Group theory and generalizations
General
213
230
10.4171/GGD/124
http://www.ems-ph.org/doi/10.4171/GGD/124