Research output: Contribution to journal › Article › peer-review
For a group G and R=Z,Z/p,Q we denote by GˆR the R-completion of G. We study the map Hn(G,K)→Hn(GˆR,K), where (R,K)=(Z,Z/p),(Z/p,Z/p),(Q,Q). We prove that H2(G,K)→H2(GˆR,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(GˆR,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.
Original language | English |
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Pages (from-to) | 473-502 |
Number of pages | 30 |
Journal | Journal of Algebra |
Volume | 501 |
DOIs | |
State | Published - 1 May 2018 |
ID: 46234097