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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Asymptotic dimension of finitely presented groups


Author: Thanos Gentimis
Journal: Proc. Amer. Math. Soc. 136 (2008), 4103-4110
MSC (2000): Primary 20F65, 20F69
Published electronically: July 17, 2008
MathSciNet review: 2431020
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Abstract: We prove that if a finitely presented group is one-ended, then its asymptotic dimension is greater than $ 1$. It follows that a finitely presented group of asymptotic dimension $ 1$ is virtually free.


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Additional Information

Thanos Gentimis
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: thanos@ufl.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-08973-9
PII: S 0002-9939(08)08973-9
Keywords: Dimension theory, asymptotic dimension, finitely presented group
Received by editor(s): August 15, 2005
Received by editor(s) in revised form: August 29, 2006
Published electronically: July 17, 2008
Additional Notes: Research supported by the program ’EPEAEK-Pythagoras’ (75% European grant, 25% Greek national grant)
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.