A finitely presented group with unbounded dead-end depth

Details A finitely presented group with unbounded dead-end depth A finitely presented group with unbounded dead-end depth

2004-06-22

arxiv.org/abs/math/0406443v3

Proc. Amer. Math. Soc., 134(2), pages 343-349, 2006

Mathematics

Group Theory

10 pages, 3 figures

Scientific paper

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.

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