A finitely presented group with infinite dead end depth
Sean Cleary, Tim Riley · arXiv (Cornell University) · 2004
The dead end depth of an element g of a group G with finite generating set A is the distance from g to the complement of the radius dA(1,g) closed ball, in the word metric dA defined with respect to A. We say that G has infinite dead end depth when dead end depth is unbounded, ranging over G. We exhibit a finitely presented group G with a finite generating set, with respect to which G has infinite dead end depth.