English

The unbounded dead-end depth property is not a group invariant

Group Theory 2010-08-12 v2

Abstract

The dead-end depth of an element g of a group with finite generating set A is the distance from g to the complement of the radius d(1,g) closed ball, in the word metric d associated to A. We exhibit a finitely presented group K with two finite generating sets A and B such that dead-end depth is unbounded on K with respect to A but is at most two with respect to B.

Keywords

Cite

@article{arxiv.math/0504121,
  title  = {The unbounded dead-end depth property is not a group invariant},
  author = {Tim R. Riley and Andrew D. Warshall},
  journal= {arXiv preprint arXiv:math/0504121},
  year   = {2010}
}

Comments

16 pages, 5 figures

R2 v1 2026-07-22T17:17:49.005Z