Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896280 | Journal of Algebra | 2018 | 30 Pages |
Abstract
For a group G and R=Z,Z/p,Q we denote by GËR the R-completion of G. We study the map Hn(G,K)âHn(GËR,K), where (R,K)=(Z,Z/p),(Z/p,Z/p),(Q,Q). We prove that H2(G,K)âH2(GËR,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)âHn(GËR,K) is an epimorphism for any n if G is a finitely presented group of the form G=MâC, where C is the infinite cyclic group and M is a C-module.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Sergei O. Ivanov,