{"paper":{"title":"Pro-p groups of positive deficiency","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander Schmidt, Jonathan A. Hillman","submitted_at":"2008-02-26T15:02:29Z","abstract_excerpt":"Let \\Gamma be a finitely presentable pro-p group with a nontrivial finitely generated closed normal subgroup N of infinite index. Then def(\\Gamma)\\leq 1, and if def(\\Gamma)=1 then \\Gamma is a pro-p duality group of dimension 2, N is a free pro-p group and \\Gamma/N is virtually free. In particular, if the centre of \\Gamma is nontrivial and def(\\Gamma)\\geq 1, then def(\\Gamma)=1, cd G \\leq 2 and \\Gamma is virtually a direct product F \\times Z_p, with F a finitely generated free pro-p group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.3825","kind":"arxiv","version":2},"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"}