On Bousfield's problem for solvable groups of finite Prüfer rank

الأصل · EN

For a group G and R=Z,Z/p,Q we denote by Gᵣ the R-completion of G. We study the map Hₙ(G,K)→ Hₙ(Gᵣ,K), where (R,K)=(Z,Z/p),(Z/p,Z/p),(Q,Q). We prove that H₂(G,K)→ H₂(Gᵣ,K) is an epimorphism for a finitely generated solvable group G of finite Prüfer rank. In particular, Bousfield's HK-localisation of such groups coincides with the K-completion for K=Z/p,Q. Moreover, we prove that Hₙ(G,K)→ Hₙ(Gᵣ,K) is an epimorphism for any n if G is a finitely presented group of the form G=M C, where C is the infinite cyclic group and M is a C-module.