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(A) (1, g) closed ball, in the word metric d(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 bounded above by three with respect to B.
Translated title of the contribution | The unbounded dead-end depth property is not a group invariant |
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Original language | English |
Pages (from-to) | 969 - 983 |
Number of pages | 15 |
Journal | International Journal of Algebra and Computation |
Volume | 16 (5) |
DOIs | |
Publication status | Published - Oct 2006 |