{"paper":{"title":"Bloch-Kato pro-p groups and locally powerful groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.NT"],"primary_cat":"math.GR","authors_text":"Claudio Quadrelli","submitted_at":"2012-11-19T17:14:10Z","abstract_excerpt":"A Bloch-Kato pro-p group G is a pro-p group with the property that the F_p-cohomology ring of every closed subgroup of G is quadratic. It is shown that either such a pro-p group G contains no closed free pro-p groups of infinite rank, or there exists an orientation $\\theta\\colon G\\rightarrow \\Z_p^\\times$ such that G is theta-abelian. In case that G is also finitely generated, this implies that G is powerful, p-adic analytic with d(G)=cd(G), and its \\F_p-cohomology ring is an exterior algebra. These results will be obtained by studying locally powerful groups (see Theorem A). There are certain "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4504","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"}