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Applied to a semi-direct factor $G\\to\\mathbb{Z}_p\\to G$ isomorphic to $\\mathbb{Z}_p$ which defines a non-trivial end in the sense of A.A. Korenev one concludes that the closure of the normal closure of the image of $\\sigma$ is a free pro-$p$ subgroup (cf. Thm. C). From this result we will deduce a structure th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1303.5872","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-23T18:06:02Z","cross_cats_sorted":[],"title_canon_sha256":"51d7e23e4102d8fb5188b3ff1df9962f930b0bc387dbdae7dab02f77fbf88094","abstract_canon_sha256":"a2fb5dfbcb64b9d3bb82411e41ede203ae329f5e3f005958218275f3a8c1e0f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:01.065822Z","signature_b64":"/0lVvwhmgGnh9zs241M8A9TdxyXXlZahz2DlcwBP34EQaQRWfG9i7rYpcKmcPGT3xoERZ336ZnupkCO+wuW+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac60b1878dc507919eb522a528bef59987f0f71876df83598813e3698d344592","last_reissued_at":"2026-05-18T03:30:01.065201Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:01.065201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The projective dimension of profinite modules for pro-p groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Thomas Weigel","submitted_at":"2013-03-23T18:06:02Z","abstract_excerpt":"The homology groups introduced by A. Brumer can be used to establish a criterion ensuring that a profinite $\\mathbb{F}_p[[G]]$-module of a pro-$p$ group $G$ has projective dimension $d<\\infty$ (cf. Thm. A). This criterion yields a new characterization of free pro-$p$ groups (cf. Cor. B). Applied to a semi-direct factor $G\\to\\mathbb{Z}_p\\to G$ isomorphic to $\\mathbb{Z}_p$ which defines a non-trivial end in the sense of A.A. Korenev one concludes that the closure of the normal closure of the image of $\\sigma$ is a free pro-$p$ subgroup (cf. Thm. C). 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