Embeddings of relatively free groups into finitely presented groups

2000/05/11 by A. Yu. Olshanskii, Olshanskii, A. Yu., Mark Sapir +2
Computer Science · Mathematics · #Authorship Attribution and Profiling #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.math/0005112

arxiv created 2000/05/11 · openalex publication_date 2000/05/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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