Embeddings of relatively free groups into finitely presented groups (Q2704358)

Two theorems are proved. Theorem 1.2. Let \(f(n)\) be the verbal isoperimetric function of a group variety \(V\) defined by the identity \(v=1\). Then the free group \(F_m(V)\) of rank \(m\) in the variety \(V\) can be isomorphically embedded into a finitely presented group \(H=H(v,m)\) with isoperimetric function \(n^2f(n^2)^2\). The presentation of \(H\) is explicitly constructed given the word \(v\), and the embedding is quasi-isometric. Theorem 1.3. The Baumslag-Solitar group \(BS_{k,1}=\langle a,b\mid b^{-1}ab=a^k\rangle\) is quasi-isometric embeddable into a finitely presented group \(H_{k,1}\) with isoperimetric function \(n^{10}\).NEWLINENEWLINEFor the entire collection see [Zbl 0953.00031].