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.
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