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The Dehn function of Baumslag's metabelian group
Martin Kassabov and Tim Riley Geometriae Dedicata, Volume 158, Issue 1, pages 109–119, 2012 Baumslag's group is a finitely presented metabelian group with a Z–wreath–Z subgroup. There is an analogue with an additional torsion relation in which this subgroup becomes Cm–wreath–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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