{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4LGG5NE3X5QZI3SPXFRWEK3XGC","short_pith_number":"pith:4LGG5NE3","schema_version":"1.0","canonical_sha256":"e2cc6eb49bbf61946e4fb963622b7730977b5d1c5ffac74804abc6ab37de1d6b","source":{"kind":"arxiv","id":"1502.06840","version":1},"attestation_state":"computed","paper":{"title":"Maximal subgroups of finite soluble groups in general position","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrea Lucchini, Eloisa Detomi","submitted_at":"2015-02-24T15:45:51Z","abstract_excerpt":"For a finite group $G$ we investigate the difference between the maximum size MaxDim$(G)$ of an \"independent\" family of maximal subgroups of $G$ and maximum size $m(G)$ of an irredundant sequence of generators of $G$. We prove that MaxDim$(G)=m(G)$ if the derived subgroup of $G$ is nilpotent. However MaxDim$(G)-m(G)$ can be arbitrarily large: for any odd prime $p,$ we construct a finite soluble group with Fitting length 2 satisfying $m(G)=3$ and MaxDim$(G)=p.$"},"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":"1502.06840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-24T15:45:51Z","cross_cats_sorted":[],"title_canon_sha256":"531d9823ce9fac3df911d884591601ed9525617241b0900a5a810df533df76f9","abstract_canon_sha256":"172758e34fd167a3420132dd8079d60224b6395a23df2e3c2e257e9a0c43317a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:24.497158Z","signature_b64":"pWc27o0QeioosCUixjvZA8TDjsMhSuV5WdyATfXmHGFRw1rQvKQMkKHXny3HgVgsTE7UrE8w6i5ABdNB5dXoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2cc6eb49bbf61946e4fb963622b7730977b5d1c5ffac74804abc6ab37de1d6b","last_reissued_at":"2026-05-18T02:26:24.496570Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:24.496570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximal subgroups of finite soluble groups in general position","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrea Lucchini, Eloisa Detomi","submitted_at":"2015-02-24T15:45:51Z","abstract_excerpt":"For a finite group $G$ we investigate the difference between the maximum size MaxDim$(G)$ of an \"independent\" family of maximal subgroups of $G$ and maximum size $m(G)$ of an irredundant sequence of generators of $G$. We prove that MaxDim$(G)=m(G)$ if the derived subgroup of $G$ is nilpotent. However MaxDim$(G)-m(G)$ can be arbitrarily large: for any odd prime $p,$ we construct a finite soluble group with Fitting length 2 satisfying $m(G)=3$ and MaxDim$(G)=p.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06840","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":"1502.06840","created_at":"2026-05-18T02:26:24.496671+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.06840v1","created_at":"2026-05-18T02:26:24.496671+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06840","created_at":"2026-05-18T02:26:24.496671+00:00"},{"alias_kind":"pith_short_12","alias_value":"4LGG5NE3X5QZ","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4LGG5NE3X5QZI3SP","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4LGG5NE3","created_at":"2026-05-18T12:29:05.191682+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/4LGG5NE3X5QZI3SPXFRWEK3XGC","json":"https://pith.science/pith/4LGG5NE3X5QZI3SPXFRWEK3XGC.json","graph_json":"https://pith.science/api/pith-number/4LGG5NE3X5QZI3SPXFRWEK3XGC/graph.json","events_json":"https://pith.science/api/pith-number/4LGG5NE3X5QZI3SPXFRWEK3XGC/events.json","paper":"https://pith.science/paper/4LGG5NE3"},"agent_actions":{"view_html":"https://pith.science/pith/4LGG5NE3X5QZI3SPXFRWEK3XGC","download_json":"https://pith.science/pith/4LGG5NE3X5QZI3SPXFRWEK3XGC.json","view_paper":"https://pith.science/paper/4LGG5NE3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.06840&json=true","fetch_graph":"https://pith.science/api/pith-number/4LGG5NE3X5QZI3SPXFRWEK3XGC/graph.json","fetch_events":"https://pith.science/api/pith-number/4LGG5NE3X5QZI3SPXFRWEK3XGC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4LGG5NE3X5QZI3SPXFRWEK3XGC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4LGG5NE3X5QZI3SPXFRWEK3XGC/action/storage_attestation","attest_author":"https://pith.science/pith/4LGG5NE3X5QZI3SPXFRWEK3XGC/action/author_attestation","sign_citation":"https://pith.science/pith/4LGG5NE3X5QZI3SPXFRWEK3XGC/action/citation_signature","submit_replication":"https://pith.science/pith/4LGG5NE3X5QZI3SPXFRWEK3XGC/action/replication_record"}},"created_at":"2026-05-18T02:26:24.496671+00:00","updated_at":"2026-05-18T02:26:24.496671+00:00"}