English

Lower bound on growth of non-elementary subgroups in relatively hyperbolic groups

Group Theory 2021-03-18 v2 Metric Geometry

Abstract

This paper proves that in a non-elementary relatively hyperbolic group, the logarithm growth rate of any non-elementary subgroup has a linear lower bound by the logarithm of the size of the corresponding generating set. As a consequence, any non-elementary subgroup has uniform exponential growth.

Keywords

Cite

@article{arxiv.2103.02304,
  title  = {Lower bound on growth of non-elementary subgroups in relatively hyperbolic groups},
  author = {Yu-miao Cui and Yue-ping Jiang and Wen-yuan Yang},
  journal= {arXiv preprint arXiv:2103.02304},
  year   = {2021}
}

Comments

16 pages, 1 figure; some arguments clarified and references updated

R2 v1 2026-06-23T23:42:13.042Z