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|
|Pages (from-to)||969 - 983|
|Number of pages||15|
|Journal||International Journal of Algebra and Computation|
|Publication status||Published - Oct 2006|