{"paper":{"title":"On Bousfield's problem for solvable groups of finite Pr\\\"ufer rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR"],"primary_cat":"math.KT","authors_text":"Sergei O. Ivanov","submitted_at":"2017-04-07T12:55:57Z","abstract_excerpt":"For a group $G$ and $R=\\mathbb Z,\\mathbb Z/p,\\mathbb Q$ we denote by $\\hat G_R$ the $R$-completion of $G.$ We study the map $H_n(G,K)\\to H_n(\\hat G_R,K),$ where $(R,K)=(\\mathbb Z,\\mathbb Z/p),(\\mathbb Z/p,\\mathbb Z/p),(\\mathbb Q,\\mathbb Q).$ We prove that $H_2(G,K)\\to H_2(\\hat G_R,K)$ is an epimorphism for a finitely generated solvable group $G$ of finite Pr\\\"ufer rank. In particular, Bousfield's $HK$-localisation of such groups coincides with the $K$-completion for $K=\\mathbb Z/p,\\mathbb Q.$ Moreover, we prove that $H_n(G,K)\\to H_n(\\hat G_R,K)$ is an epimorphism for any $n$ if $G$ is a finite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02212","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}