Ju n 20 04 A finitely presented group with infinite dead end depth
نویسنده
چکیده
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. 2000 Mathematics Subject Classification: 20F65
منابع مشابه
The Unbounded Dead-end Depth Property Is not a Group Invariant
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 dA(1, g) closed ball, in the word metric dA. 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 bounded above by three with respect to B.
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