{"paper":{"title":"Group localization and two problems of Levine","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AT","authors_text":"Kent E. Orr, Roman Mikhailov","submitted_at":"2013-06-25T19:06:20Z","abstract_excerpt":"A. K. Bousfield's $H\\mathbb Z$-localization of groups inverts homologically two-connected homomorphisms of groups. J. P. Levine's algebraic closure of groups inverts homomorphisms between finitely generated and finitely presented groups which are homologically two-connected and for which the image normally generates. We resolve an old problem concerning Bousfield $H\\mathbb Z$-localization of groups, and answer two questions of Levine regarding algebraic closure of groups. In particular, we show that the kernel of the natural homomorphism from a group $G$ to it's Bousfield $H\\mathbb Z$-localiza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6065","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"}