Dehn Function of Finitely Presented Metabelian Groups
arXiv:2010.03637 · doi:10.1515/jgth-2020-0182
Abstract
In this paper, we compute an upper bound for the Dehn function of a finitely presented metabelian group. In addition, we prove that the same upper bound works for the relative Dehn function of a finitely generated metabelian group. We also show that every wreath product of a free abelian group of finite rank with a finitely generated abelian group can be embedded into a metabelian group with exponential Dehn function.
41 pages, 4 figures. Fix an issue with the trivial case and improve the theorem. Comments are welcome!