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A finitely presented group with unbounded dead end depth
Sean Cleary and Tim R. Riley
The dead-end depth of an element g of a group G with generating set
A is the distance from g to the complement of the radius d(1,g) closed ball, in the
word metric d defined with respect to A. We exhibit a finitely presented group G with a finite generating set with respect to which dead-end depth is unbounded.
Regrettably, the original version of this article (Proc. Amer. Math. Soc., 134(2), pages 343–349, 2006) contained a significant error. An erratum has appeared: Proc. Amer. Math. Soc. 136, 2641–2645, 2008. The following is a corrected version of the original paper (March 2007).
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