Asymptotic dimension of finitely presented groups
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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.References
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Additional Information
- Thanos Gentimis
- Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
- Email: thanos@ufl.edu
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 4103-4110
- MSC (2000): Primary 20F65, 20F69
- DOI: https://doi.org/10.1090/S0002-9939-08-08973-9
- MathSciNet review: 2431020