{"paper":{"title":"Groups with the same cohomology as their profinite completions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.GR","authors_text":"Karl Lorensen","submitted_at":"2008-02-01T13:23:45Z","abstract_excerpt":"For any positive integer $n$, $\\mathcal{A}_n$ is the class of all groups $G$ such that, for $0\\leq i\\leq n$, $H^i(\\hat{G},A)\\cong H^i(G,A)$ for every finite discrete $\\hat{G}$-module $A$. We describe certain types of free products with amalgam and HNN extensions that are in some of the classes $\\mathcal{A}_n$. In addition, we investigate the residually finite groups in the class $\\mathcal{A}_2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.0118","kind":"arxiv","version":6},"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"}