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The Dehn function of Baumslag’s metabelian group

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Abstract

Baumslag’s group is a finitely presented metabelian group with a \({\mathbb Z \wr \mathbb Z}\) subgroup. There is an analogue with an additional torsion relation in which this subgroup becomes \({C_m \wr \mathbb Z}\). We prove that Baumslag’s group has an exponential Dehn function. This contrasts with the torsion analogues which have quadratic Dehn functions.

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Author notes

  1. M. Kassabov

    Present address: School of Mathematics, University of Southampton, Highfield, Southampton, SO17 1BJ, UK

Authors and Affiliations

  1. Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, NY, 14850, USA

    M. Kassabov & T. R. Riley

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  1. M. Kassabov
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  2. T. R. Riley
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Correspondence to T. R. Riley.

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Kassabov, M., Riley, T.R. The Dehn function of Baumslag’s metabelian group. Geom Dedicata 158, 109–119 (2012). https://doi.org/10.1007/s10711-011-9623-y

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