Embeddings of relatively free groups into finitely presented groups

Details Embeddings of relatively free groups into finitely presented groups Embeddings of relatively free groups into finitely presented groups

2000-05-11

arxiv.org/abs/math/0005112v1

Mathematics

Group Theory

Scientific paper

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.

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