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

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.

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