{"paper":{"title":"Groups with the same cohomology as their pro-$p$ 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":"2008-09-18T01:17:17Z","abstract_excerpt":"For any prime $p$ and group $G$, denote the pro-$p$ completion of $G$ by $\\hat{G}^p$. Let $\\mathcal{C}$ be the class of all groups $G$ such that, for each natural number $n$ and prime number $p$, $H^n(\\hat{G^p},\\mathbb Z/p)\\cong H^n(G, \\mathbb Z/p)$, where $\\mathbb Z/p$ is viewed as a discrete, trivial $\\hat{G}^p$-module. In this article we identify certain kinds of groups that lie in $\\mathcal{C}$. In particular, we show that right-angled Artin groups are in $\\mathcal{C}$ and that this class also contains some special types of free products with amalgamation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.3046","kind":"arxiv","version":3},"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"}