TY - JOUR

T1 - On Bousfield's problem for solvable groups of finite Prüfer rank

AU - Ivanov, Sergei O.

PY - 2018/5/1

Y1 - 2018/5/1

N2 - 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.

AB - 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.

KW - Bousfield's problem

KW - HR-localisation of groups

KW - Prüfer rank

KW - R-completion of groups

KW - Solvable groups

UR - http://www.scopus.com/inward/record.url?scp=85056317992&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2018.01.016

DO - 10.1016/j.jalgebra.2018.01.016

M3 - Article

AN - SCOPUS:85056317992

VL - 501

SP - 473

EP - 502

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -