The unbounded dead-end depth property is not a group invariant

Details The unbounded dead-end depth property is not a group invariant The unbounded dead-end depth property is not a group invariant

2005-04-06

arxiv.org/abs/math/0504121v2

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

Mathematics

Group Theory

16 pages, 5 figures

Scientific paper

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 associated to A. 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 two with respect to B.

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