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

2021/03/03 by Yu-miao Cui, Cui, Yu-miao, Yue-Ping Jiang +3
Mathematics · #20F67 #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Primary 20F65

paper · pdf · doi:10.48550/arxiv.2103.02304

openalex publication_date 2021/03/03 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28

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.

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• Relative growth in hyperbolic groups
• Growth of relatively hyperbolic groups
• Extensions of hyperbolic groups have locally uniform exponential growth
• Growth gaps and exponential genericity in acylindrically hyperbolic groups
• Uniform exponential growth for groups with proper product actions on hyperbolic spaces