English

Embeddings of relatively free groups into finitely presented groups

Group Theory 2007-05-23 v1

Abstract

We construct easy embeddings of relatively free groups (say the free Burnside group, the free solvable group) into finitely presented groups. We introduce a concept of verbal isoperimetric function of a group variety. We prove that if the verbal Dehn function of a relatively free group is bounded by a polynomial then the group can be embedded quasi-isometrically into a finitely presented group with polynomial isoperimetric function. We also construct an easy embedding of any Baumslag-Solitar solvable group into a finitely presented group with polynomial Dehn function.

Keywords

Cite

@article{arxiv.math/0005112,
  title  = {Embeddings of relatively free groups into finitely presented groups},
  author = {A. Yu. Olshanskii and M. V. Sapir},
  journal= {arXiv preprint arXiv:math/0005112},
  year   = {2007}
}
R2 v1 2026-07-22T16:32:39.158Z