## 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 |