Dmitry Matsnev (2008)
Colloquium Mathematicae
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We show that one relator groups viewed as metric spaces with respect to the word-length metric have finite asymptotic dimension in the sense of Gromov, and we give an improved estimate of that dimension in terms of the relator length. The construction is similar to one of Bell and Dranishnikov, but we produce a sharper estimate.
Ol'shanskii, A.Yu., Sapir, M.V. (2003)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Baumslag, Gilbert, Cleary, Sean, Havas, George (2004)
Experimental Mathematics
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Nataša Božović (1985)
Publications de l'Institut Mathématique
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Justin Smith (2007)
Revista Matemática Complutense
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We describe a sufficient condition for a finitely generated group to have infinite asymptotic dimension. As an application, we conclude that the first Grigorchuk group has infinite asymptotic dimension.
Avinoam Mann (1996)
Forum mathematicum
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Plesken, Wilhelm, Schulz, Tilman (2000)
Experimental Mathematics
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Gehring, F.W., Martin, G.J. (1996)
Annales Academiae Scientiarum Fennicae. Mathematica
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Ol'shanskij, A.Yu., Sapir, M.V. (2001)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Petersen, Carsten Lunde (1993)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Yang Kok Kim (1996)
Rendiconti del Seminario Matematico della Università di Padova
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Christophe Pittet (1995)
Revista Matemática Iberoamericana
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The isoperimetric inequality |∂Ω| / |Ω| = constant / log |Ω| for finite subsets Ω in a finitely generated group Γ with exponential growth is optimal if Γ is polycyclic.
S. Lajos (1964)
Matematički Vesnik
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