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The unbounded dead end depth property is not a group invariant

Tim Riley and Andrew Warshall

Int. J. Alg. Comp., 16(5), pages 969–984, 2006

The dead-end depth of an element g of a group with finite generating set A is the distance from g to the complement of the radius d(1,g) closed ball, in the word metric d. We exhibit a finitely presented group K with two finite generating sets A and B such that dead-end depth is unbounded on K with respect to A but is at most three with respect to B.

14 pages, 5 figures.