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Then all the flabby (resp.\\ coflabby) $R\\pi$-lattices are invertible if and only if all the Sylow subgroups of $\\pi$ are cyclic. The above theorem was proved by Endo and Miyata when $R=\\bm{Z}$ \\cite[Theorem 1.5]{EM}. As applications of this theorem, we give a short proof and a partial generalization of a result of Torrecillas and Weigel \\cite[Theorem A]{TW}, "},"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":"1408.4223","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-19T06:44:36Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"e395ac90085594667087da2102101a5c0e8aa7bd54279ec87fea3bcbb445ad4e","abstract_canon_sha256":"685b607da2b24ae6fb5ed826c8a4ed06cd395875a8f1a740298cb13ba1f40e1e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:55.849101Z","signature_b64":"csWAadmlGSPQkBl6HggvMpT/JhrPHgGrGn6R6t+ajYV54vm33CJbV7lthDVy2uu9Lrk8qzpAJwCXM1MriUa5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b2597c523a43b37c11214478cc8415b42fff8f493183ef3720c73c392017fcf","last_reissued_at":"2026-05-18T02:44:55.848614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:55.848614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invertible Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.NT","authors_text":"Esther Beneish, Ming-chang Kang","submitted_at":"2014-08-19T06:44:36Z","abstract_excerpt":"Theorem. Let $\\pi$ be a finite group of order $n$, $R$ be a Dedekind domain satisfying that (i) $\\fn{char}R=0$, (ii) every prime divisor of $n$ is not invertible in $R$, and (iii) $p$ is unramified in $R$ for any prime divisor $p$ of $n$. Then all the flabby (resp.\\ coflabby) $R\\pi$-lattices are invertible if and only if all the Sylow subgroups of $\\pi$ are cyclic. The above theorem was proved by Endo and Miyata when $R=\\bm{Z}$ \\cite[Theorem 1.5]{EM}. As applications of this theorem, we give a short proof and a partial generalization of a result of Torrecillas and Weigel \\cite[Theorem A]{TW}, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4223","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.4223","created_at":"2026-05-18T02:44:55.848692+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.4223v1","created_at":"2026-05-18T02:44:55.848692+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4223","created_at":"2026-05-18T02:44:55.848692+00:00"},{"alias_kind":"pith_short_12","alias_value":"NMSZPRJDUQ5T","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NMSZPRJDUQ5TPQIS","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NMSZPRJD","created_at":"2026-05-18T12:28:41.024544+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NMSZPRJDUQ5TPQISCRDYZSCBLN","json":"https://pith.science/pith/NMSZPRJDUQ5TPQISCRDYZSCBLN.json","graph_json":"https://pith.science/api/pith-number/NMSZPRJDUQ5TPQISCRDYZSCBLN/graph.json","events_json":"https://pith.science/api/pith-number/NMSZPRJDUQ5TPQISCRDYZSCBLN/events.json","paper":"https://pith.science/paper/NMSZPRJD"},"agent_actions":{"view_html":"https://pith.science/pith/NMSZPRJDUQ5TPQISCRDYZSCBLN","download_json":"https://pith.science/pith/NMSZPRJDUQ5TPQISCRDYZSCBLN.json","view_paper":"https://pith.science/paper/NMSZPRJD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.4223&json=true","fetch_graph":"https://pith.science/api/pith-number/NMSZPRJDUQ5TPQISCRDYZSCBLN/graph.json","fetch_events":"https://pith.science/api/pith-number/NMSZPRJDUQ5TPQISCRDYZSCBLN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NMSZPRJDUQ5TPQISCRDYZSCBLN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NMSZPRJDUQ5TPQISCRDYZSCBLN/action/storage_attestation","attest_author":"https://pith.science/pith/NMSZPRJDUQ5TPQISCRDYZSCBLN/action/author_attestation","sign_citation":"https://pith.science/pith/NMSZPRJDUQ5TPQISCRDYZSCBLN/action/citation_signature","submit_replication":"https://pith.science/pith/NMSZPRJDUQ5TPQISCRDYZSCBLN/action/replication_record"}},"created_at":"2026-05-18T02:44:55.848692+00:00","updated_at":"2026-05-18T02:44:55.848692+00:00"}