A finitely presented group with unbounded dead-end depth
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- by Sean Cleary and Tim R. Riley
- Proc. Amer. Math. Soc. 134 (2006), 343-349
- DOI: https://doi.org/10.1090/S0002-9939-05-08043-3
- Published electronically: August 12, 2005
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Erratum: Proc. Amer. Math. Soc. 136 (2008), 2641-2645.
Abstract:
The dead-end depth of an element $g$ of a group $G$, with respect to a generating set $\mathcal {A}$, is the distance from $g$ to the complement of the radius $d_{\mathcal {A}}(1,g)$ closed ball, in the word metric $d_{\mathcal {A}}$ defined with respect to $\mathcal {A}$. 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.References
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Bibliographic Information
- Sean Cleary
- Affiliation: Department of Mathematics, The City College of New York, City University of New York, New York, New York 10031
- Email: cleary@sci.ccny.cuny.edu
- Tim R. Riley
- Affiliation: Department of Mathematics, Yale University, 10 Hillhouse Avenue, P.O. Box 208283, New Haven, Connecticut 06520-8283
- Address at time of publication: Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
- MR Author ID: 691109
- Email: tim.riley@yale.edu
- Received by editor(s): July 26, 2004
- Received by editor(s) in revised form: September 18, 2004
- Published electronically: August 12, 2005
- Additional Notes: Support for the first author from PSC-CUNY grant #65752 is gratefully acknowledged.
Support for the second author from NSF grant 0404767 is gratefully acknowledged. - Communicated by: Alexander N. Dranishnikov
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 343-349
- MSC (2000): Primary 20F65
- DOI: https://doi.org/10.1090/S0002-9939-05-08043-3
- MathSciNet review: 2176000