The rank gradient from a combinatorial viewpoint
群论
2011-02-16 v3
摘要
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.
引用
@article{arxiv.math/0701925,
title = {The rank gradient from a combinatorial viewpoint},
author = {Miklos Abert and Andrei Jaikin-Zapirain and Nikolay Nikolov},
journal= {arXiv preprint arXiv:math/0701925},
year = {2011}
}
备注
corrected some typos, to appear in Groups, Geometry and Dynamics