## Abstract

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 |
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Original language | English |

Pages (from-to) | 343 - 349 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 134 (2) |

DOIs | |

Publication status | Published - Aug 2006 |