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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1704.02212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2017-04-07T12:55:57Z","cross_cats_sorted":["math.AT","math.GR"],"title_canon_sha256":"ec2153935e03d28fe42809d8df5184320709a8df6f7b3e7ea09b6590124d9cf7","abstract_canon_sha256":"71fa3b13f34ef810369b3443e53dffd7a51ba873190db9b62b78150079b8553b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:50.400588Z","signature_b64":"KDoQJMNbcss9z6IKwlwATwcDR/nHJpakuUnKJ82bfbfuSBJYiWq8OO32isSc0K3bWevgpOKaui4mCNR5+G2rBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d46f78e330819de145c8944a97b5e2d955925164cc61fcb73d1386af6874bbd","last_reissued_at":"2026-05-18T00:46:50.399982Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:50.399982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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