The rank gradient from a combinatorial viewpoint
نویسندگان
چکیده
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.
منابع مشابه
3 1 Ja n 20 07 The rank gradient from a combinatorial viewpoint
This note investigates the asymptotic behaviour of the minimal number of generators of finite index subgroups for three natural classes of groups: amenable groups, groups possessing an infinite soluble normal subgroup and virtually free groups.
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