{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:BC7BACNH5PUVOLIK7XZG5GQVHW","short_pith_number":"pith:BC7BACNH","schema_version":"1.0","canonical_sha256":"08be1009a7ebe9572d0afdf26e9a153d9854812fc63fa26775e79812546f9c2a","source":{"kind":"arxiv","id":"2305.16254","version":3},"attestation_state":"computed","paper":{"title":"On finite $d$-maximal groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrea Lucchini, Luca Sabatini, Mima Stanojkovski","submitted_at":"2023-05-25T17:09:58Z","abstract_excerpt":"Let $d$ be a positive integer. A finite group is called $d$-maximal if it can be generated by precisely $d$ elements, while its proper subgroups have smaller generating sets. For $d\\in\\{1,2\\}$, the $d$-maximal groups have been classified up to isomorphism and only partial results have been proven for larger $d$. In this work, we prove that a $d$-maximal group is supersolvable and we give a characterization of $d$-maximality in terms of so-called maximal $(p,q)$-pairs. Moreover, we classify the maximal $(p,q)$-pairs of small rank obtaining, as a consequence, a full classification of the isomorp"},"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":"2305.16254","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2023-05-25T17:09:58Z","cross_cats_sorted":[],"title_canon_sha256":"5f94a68210da480d6942397255aec209b3667bffbcb00264a2293140e2e9c5dc","abstract_canon_sha256":"e7d0b0a81ff30841034e5ea51cb31115497b6a745bcd8c1900129a1b9ac588f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:10:21.478830Z","signature_b64":"idO+1eFLGBsWlA7kvulPDUxOS52a05wfzM4Tcj4AU4yKkwoiopWEy4nnh5akcW07/AkEsYyNELng1kUESOkXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08be1009a7ebe9572d0afdf26e9a153d9854812fc63fa26775e79812546f9c2a","last_reissued_at":"2026-07-05T10:10:21.478332Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:10:21.478332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On finite $d$-maximal groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrea Lucchini, Luca Sabatini, Mima Stanojkovski","submitted_at":"2023-05-25T17:09:58Z","abstract_excerpt":"Let $d$ be a positive integer. A finite group is called $d$-maximal if it can be generated by precisely $d$ elements, while its proper subgroups have smaller generating sets. For $d\\in\\{1,2\\}$, the $d$-maximal groups have been classified up to isomorphism and only partial results have been proven for larger $d$. In this work, we prove that a $d$-maximal group is supersolvable and we give a characterization of $d$-maximality in terms of so-called maximal $(p,q)$-pairs. Moreover, we classify the maximal $(p,q)$-pairs of small rank obtaining, as a consequence, a full classification of the isomorp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.16254","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.16254/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2305.16254","created_at":"2026-07-05T10:10:21.478391+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.16254v3","created_at":"2026-07-05T10:10:21.478391+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.16254","created_at":"2026-07-05T10:10:21.478391+00:00"},{"alias_kind":"pith_short_12","alias_value":"BC7BACNH5PUV","created_at":"2026-07-05T10:10:21.478391+00:00"},{"alias_kind":"pith_short_16","alias_value":"BC7BACNH5PUVOLIK","created_at":"2026-07-05T10:10:21.478391+00:00"},{"alias_kind":"pith_short_8","alias_value":"BC7BACNH","created_at":"2026-07-05T10:10:21.478391+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/BC7BACNH5PUVOLIK7XZG5GQVHW","json":"https://pith.science/pith/BC7BACNH5PUVOLIK7XZG5GQVHW.json","graph_json":"https://pith.science/api/pith-number/BC7BACNH5PUVOLIK7XZG5GQVHW/graph.json","events_json":"https://pith.science/api/pith-number/BC7BACNH5PUVOLIK7XZG5GQVHW/events.json","paper":"https://pith.science/paper/BC7BACNH"},"agent_actions":{"view_html":"https://pith.science/pith/BC7BACNH5PUVOLIK7XZG5GQVHW","download_json":"https://pith.science/pith/BC7BACNH5PUVOLIK7XZG5GQVHW.json","view_paper":"https://pith.science/paper/BC7BACNH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.16254&json=true","fetch_graph":"https://pith.science/api/pith-number/BC7BACNH5PUVOLIK7XZG5GQVHW/graph.json","fetch_events":"https://pith.science/api/pith-number/BC7BACNH5PUVOLIK7XZG5GQVHW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BC7BACNH5PUVOLIK7XZG5GQVHW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BC7BACNH5PUVOLIK7XZG5GQVHW/action/storage_attestation","attest_author":"https://pith.science/pith/BC7BACNH5PUVOLIK7XZG5GQVHW/action/author_attestation","sign_citation":"https://pith.science/pith/BC7BACNH5PUVOLIK7XZG5GQVHW/action/citation_signature","submit_replication":"https://pith.science/pith/BC7BACNH5PUVOLIK7XZG5GQVHW/action/replication_record"}},"created_at":"2026-07-05T10:10:21.478391+00:00","updated_at":"2026-07-05T10:10:21.478391+00:00"}