{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VEY3Z4BRGOHZUMUMMODMKNL7QW","short_pith_number":"pith:VEY3Z4BR","schema_version":"1.0","canonical_sha256":"a931bcf031338f9a328c6386c5357f85af6e4db375c1564d859153a1b2c12760","source":{"kind":"arxiv","id":"1611.05662","version":2},"attestation_state":"computed","paper":{"title":"The multiple holomorph of a finitely generated abelian group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"A. Caranti, F. Dalla Volta","submitted_at":"2016-11-17T12:49:17Z","abstract_excerpt":"W.H.~Mills has determined, for a finitely generated abelian group $G$, the regular subgroups $N \\cong G$ of $S(G)$, the group of permutations on the set $G$, which have the same holomorph of $G$, that is, such that $N_{S(G)}(N) = N_{S(G)}(\\rho(G))$, where $\\rho$ is the (right) regular representation.\n  We give an alternative approach to Mills' result, which relies on a characterization of the regular subgroups of $N_{S(G)}(\\rho(G))$ in terms of commutative ring structures on $G$.\n  We are led to solve, for the case of a finitely generated abelian group $G$, the following problem: given an abel"},"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":"1611.05662","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-17T12:49:17Z","cross_cats_sorted":[],"title_canon_sha256":"b84f714be11386704bcd33efced1e192b2a6d2edf0a1871e89b106531b99379e","abstract_canon_sha256":"797fdc2f30a02f2ecd9cd110ed7273c705969075816eeec962976bfd698345c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:32.535512Z","signature_b64":"3v7MvdDXvTHfVtTTmQyCbaf58PF/jwrnEWr0MYAdHdlMrvFkWPUIcEBVG+So+xO9o5NloBjF3i0pGBpDeW3vCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a931bcf031338f9a328c6386c5357f85af6e4db375c1564d859153a1b2c12760","last_reissued_at":"2026-05-18T00:48:32.535085Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:32.535085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The multiple holomorph of a finitely generated abelian group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"A. Caranti, F. Dalla Volta","submitted_at":"2016-11-17T12:49:17Z","abstract_excerpt":"W.H.~Mills has determined, for a finitely generated abelian group $G$, the regular subgroups $N \\cong G$ of $S(G)$, the group of permutations on the set $G$, which have the same holomorph of $G$, that is, such that $N_{S(G)}(N) = N_{S(G)}(\\rho(G))$, where $\\rho$ is the (right) regular representation.\n  We give an alternative approach to Mills' result, which relies on a characterization of the regular subgroups of $N_{S(G)}(\\rho(G))$ in terms of commutative ring structures on $G$.\n  We are led to solve, for the case of a finitely generated abelian group $G$, the following problem: given an abel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05662","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.05662","created_at":"2026-05-18T00:48:32.535148+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.05662v2","created_at":"2026-05-18T00:48:32.535148+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05662","created_at":"2026-05-18T00:48:32.535148+00:00"},{"alias_kind":"pith_short_12","alias_value":"VEY3Z4BRGOHZ","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VEY3Z4BRGOHZUMUM","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VEY3Z4BR","created_at":"2026-05-18T12:30:48.956258+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/VEY3Z4BRGOHZUMUMMODMKNL7QW","json":"https://pith.science/pith/VEY3Z4BRGOHZUMUMMODMKNL7QW.json","graph_json":"https://pith.science/api/pith-number/VEY3Z4BRGOHZUMUMMODMKNL7QW/graph.json","events_json":"https://pith.science/api/pith-number/VEY3Z4BRGOHZUMUMMODMKNL7QW/events.json","paper":"https://pith.science/paper/VEY3Z4BR"},"agent_actions":{"view_html":"https://pith.science/pith/VEY3Z4BRGOHZUMUMMODMKNL7QW","download_json":"https://pith.science/pith/VEY3Z4BRGOHZUMUMMODMKNL7QW.json","view_paper":"https://pith.science/paper/VEY3Z4BR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.05662&json=true","fetch_graph":"https://pith.science/api/pith-number/VEY3Z4BRGOHZUMUMMODMKNL7QW/graph.json","fetch_events":"https://pith.science/api/pith-number/VEY3Z4BRGOHZUMUMMODMKNL7QW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VEY3Z4BRGOHZUMUMMODMKNL7QW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VEY3Z4BRGOHZUMUMMODMKNL7QW/action/storage_attestation","attest_author":"https://pith.science/pith/VEY3Z4BRGOHZUMUMMODMKNL7QW/action/author_attestation","sign_citation":"https://pith.science/pith/VEY3Z4BRGOHZUMUMMODMKNL7QW/action/citation_signature","submit_replication":"https://pith.science/pith/VEY3Z4BRGOHZUMUMMODMKNL7QW/action/replication_record"}},"created_at":"2026-05-18T00:48:32.535148+00:00","updated_at":"2026-05-18T00:48:32.535148+00:00"}