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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A finitely presented group with unbounded dead-end depth

Authors: Sean Cleary and Tim R. Riley
Journal: Proc. Amer. Math. Soc. 134 (2006), 343-349
MSC (2000): Primary 20F65
Published electronically: August 12, 2005
Erratum: Proc. Amer. Math. Soc. 136 (2008), 2641--2645
MathSciNet review: 2176000
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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.

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Additional Information

Sean Cleary
Affiliation: Department of Mathematics, The City College of New York, City University of New York, New York, New York 10031

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

Keywords: Dead-end depth, lamplighter
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
Article copyright: © Copyright 2005 American Mathematical Society