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We prove that the intersection of a pair of finitely generated closed subgroups of a Demushkin group is finitely generated (giving an explicit bound on the number of generators). Furthermore, we show that these properties of Demushkin groups are preserved under free pro-$p$ products, and deduce that Howson's theorem holds for the Sylow subgro"},"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":"1705.09096","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-25T09:08:52Z","cross_cats_sorted":[],"title_canon_sha256":"e632f3f1fc512f89b0374b389a21b85a0d34f3b1f6350b403b1b83cb5bd8f89d","abstract_canon_sha256":"36f4d01c3669253a9c45f44ba35f9918b767d9cb2d738c44b7fd7e5a7520a093"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:40.439488Z","signature_b64":"ubv+gm/KYY6t46YMwKOeks8MFta1oDBmcATneGNWzZfLafZKNsyhnEpSV2fSMR8zL5xCx5wh2qV5UTqKF78IAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58d6e3dae4cee92b38d0dad0575f762295880ec4ab51ed4e73dbf43669ce446d","last_reissued_at":"2026-05-18T00:43:40.438968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:40.438968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Virtual retraction and Howson's theorem in pro-$p$ groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mark Shusterman, Pavel Zalesskii","submitted_at":"2017-05-25T09:08:52Z","abstract_excerpt":"We show that for every finitely generated closed subgroup $K$ of a non-solvable Demushkin group $G$, there exists an open subgroup $U$ of $G$ containing $K$, and a continuous homomorphism $\\tau \\colon U \\to K$ satisfying $\\tau(k) = k$ for every $k \\in K$. 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