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

TR Riley; AD Warshall

doi:10.1142/S0218196706003347

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

TR Riley
, AD Warshall

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

12 Citations (Scopus)

Abstract

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(A) (1, g) closed ball, in the word metric d(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 bounded above by three with respect to B.

Translated title of the contribution	The unbounded dead-end depth property is not a group invariant
Original language	English
Pages (from-to)	969 - 983
Number of pages	15
Journal	International Journal of Algebra and Computation
Volume	16 (5)
DOIs	https://doi.org/10.1142/S0218196706003347
Publication status	Published - Oct 2006

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Publisher: World Scientific Publ Co Pte Ltd

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http://www.ams.org/mathscinet/pdf/2274725.pdf?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=TI&pg6=PC&pg7=ALLF&pg8=ET&s4=riley%2C%20t%2A&s5=&s6=&s7=&s8=All&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=3

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abstract = "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(A) (1, g) closed ball, in the word metric d(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 bounded above by three with respect to B.",

author = "TR Riley and AD Warshall",

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AU - Warshall, AD

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N2 - 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(A) (1, g) closed ball, in the word metric d(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 bounded above by three with respect to B.

AB - 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(A) (1, g) closed ball, in the word metric d(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 bounded above by three with respect to B.

U2 - 10.1142/S0218196706003347

DO - 10.1142/S0218196706003347

M3 - Article (Academic Journal)

SN - 1793-6500

VL - 16 (5)

SP - 969

EP - 983

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

ER -

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

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