The dead-end depth of an element g of a group G, with respect to a 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) defined with respect to A. We exhibit a finitely presented group G with a finite generating set with respect to which there is no upper bound on the dead-end depth of elements.
|Translated title of the contribution||A finitely presented group with unbounded dead-end depth|
|Pages (from-to)||343 - 349|
|Number of pages||7|
|Journal||Proceedings of the American Mathematical Society|
|Publication status||Published - Aug 2006|