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.
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