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A finitely presented group with unbounded dead end depth

Sean Cleary and Tim R. Riley

Original version: Proc. Amer. Math. Soc., 134(2), pages 343–349, 2006.
Erratum: Proc. Amer. Math. Soc., 136, 2641–2645, 2008.
The version below is a corrected form of the original paper (March 2007).

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.