The rank gradient from a combinatorial viewpoint

Details The rank gradient from a combinatorial viewpoint The rank gradient from a combinatorial viewpoint

2007-01-31

arxiv.org/abs/math/0701925v3

Mathematics

Group Theory

corrected some typos, to appear in Groups, Geometry and Dynamics

Scientific paper

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.

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