  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.
  The authors regret that the published version of this article (Proc. Amer.
Math. Soc., 134(2), pp.343-349, 2006) contains a significant error concerning
the model for G described in Section 2. We are grateful to Jorg Lehnert for
pointing out our mistake. In this corrected version, that model has been
overhauled, and that has necessitated a number of changes in the subsequent
arguments.

Group Theory