Metabelian groups with quadratic Dehn function and Baumslag-Solitar groups

Abstract

We prove that groups in a certain class of metabelian locally compact groups, have quadratic Dehn function. As an application, we embed the solvable Baumslag-Solitar groups into finitely presented metabelian groups with quadratic Dehn function. Also, we prove that Baumslag's finitely presented metabelian groups, in which the lamplighter groups embed, have quadratic Dehn function.

13 pages, one figure. v1->v2: title has been changed; added application to Baumslag's group v2->v3 numerous corrections

References in corpus (2)

• Dimension of asymptotic cones of Lie groups
• The Dehn function of Baumslag's Metabelian Group

Cited by in corpus (9)

• Dehn function and asymptotic cones of Abels' group
• Geometric presentations of Lie groups and their Dehn functions
• Lipschitz connectivity and filling invariants in solvable groups and buildings
• Cone-equivalent nilpotent groups with different Dehn functions
• Lamplighters, Metabelian Groups, and Horocyclic Products of Trees
• The Dehn function of Baumslag's Metabelian Group
• Undistorted embeddings of metabelian groups of finite Prüfer rank
• Dehn functions of higher rank arithmetic groups of type $A_n$ in products of simple Lie groups
• Dehn Function of Finitely Presented Metabelian Groups