English

Dehn Function of Finitely Presented Metabelian Groups

Group Theory 2022-10-27 v3

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.

Keywords

Cite

@article{arxiv.2010.03637,
  title  = {Dehn Function of Finitely Presented Metabelian Groups},
  author = {Wenhao Wang},
  journal= {arXiv preprint arXiv:2010.03637},
  year   = {2022}
}

Comments

41 pages, 4 figures. Fix an issue with the trivial case and improve the theorem. Comments are welcome!

R2 v1 2026-06-23T19:08:49.124Z