Israel Journal of Mathematics

, Volume 132, Issue 1, pp 373–380 | Cite as

On the geometry of infinite cyclic subgroups

  • Anna Erschler-Dyubina


In this paper we construct an example of a word metric on an infinite cyclic subgroup. This example shows that subexponential distortion does not obstruct non-trivial growth of connected radii. This answers a question of Gromov [6]. The constructed metric has other pathological properies. Specifically, its asymptotic cone depends on the choice of ultrafilter and scaling sequence.


Cayley Graph Cyclic Subgroup London Mathematical Society Hyperbolic Group Distortion Function 
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Copyright information

© Hebrew University 2002

Authors and Affiliations

  1. 1.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

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