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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.

Gilbert Baumslag Max Dehn