{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YB5NY6JO2ZFY4HKDPBTTWRKTVJ","short_pith_number":"pith:YB5NY6JO","schema_version":"1.0","canonical_sha256":"c07adc792ed64b8e1d4378673b4553aa4eb83e0a2dc6e1ac47677f8d42537a0a","source":{"kind":"arxiv","id":"1402.0366","version":2},"attestation_state":"computed","paper":{"title":"On a conjecture of Gluck","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Attila Mar\\'oti, Hung Ngoc Nguyen, James P. Cossey, Zolt\\'an Halasi","submitted_at":"2014-02-03T12:41:37Z","abstract_excerpt":"Let $F(G)$ and $b(G)$ respectively denote the Fitting subgroup and the largest degree of an irreducible complex character of a finite group $G$. A well-known conjecture of D. Gluck claims that if $G$ is solvable then $|G:F(G)|\\leq b(G)^{2}$. We confirm this conjecture in the case where $|F(G)|$ is coprime to 6. We also extend the problem to arbitrary finite groups and prove several results showing that the largest irreducible character degree of a finite group strongly controls the group structure."},"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":"1402.0366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-03T12:41:37Z","cross_cats_sorted":[],"title_canon_sha256":"bf4eb66cb1e370b2a1f238c320aa837a505d318c7068c82dfd11665bac882ec0","abstract_canon_sha256":"65b9ca9310e33812034963925c782278a89a583820101adfb157eac9dde47b2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:08.121730Z","signature_b64":"BPaVnv36crTC6CcFj9IrbKcmD4uQN/yD0BRBFUpGeh9Axjuw3YCZmBXwgg9fLIhRAFbV9ufdMXkD5AiH6ueaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c07adc792ed64b8e1d4378673b4553aa4eb83e0a2dc6e1ac47677f8d42537a0a","last_reissued_at":"2026-05-18T02:42:08.121116Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:08.121116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a conjecture of Gluck","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Attila Mar\\'oti, Hung Ngoc Nguyen, James P. Cossey, Zolt\\'an Halasi","submitted_at":"2014-02-03T12:41:37Z","abstract_excerpt":"Let $F(G)$ and $b(G)$ respectively denote the Fitting subgroup and the largest degree of an irreducible complex character of a finite group $G$. A well-known conjecture of D. Gluck claims that if $G$ is solvable then $|G:F(G)|\\leq b(G)^{2}$. We confirm this conjecture in the case where $|F(G)|$ is coprime to 6. We also extend the problem to arbitrary finite groups and prove several results showing that the largest irreducible character degree of a finite group strongly controls the group structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0366","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":"1402.0366","created_at":"2026-05-18T02:42:08.121208+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.0366v2","created_at":"2026-05-18T02:42:08.121208+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0366","created_at":"2026-05-18T02:42:08.121208+00:00"},{"alias_kind":"pith_short_12","alias_value":"YB5NY6JO2ZFY","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YB5NY6JO2ZFY4HKD","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YB5NY6JO","created_at":"2026-05-18T12:28:57.508820+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/YB5NY6JO2ZFY4HKDPBTTWRKTVJ","json":"https://pith.science/pith/YB5NY6JO2ZFY4HKDPBTTWRKTVJ.json","graph_json":"https://pith.science/api/pith-number/YB5NY6JO2ZFY4HKDPBTTWRKTVJ/graph.json","events_json":"https://pith.science/api/pith-number/YB5NY6JO2ZFY4HKDPBTTWRKTVJ/events.json","paper":"https://pith.science/paper/YB5NY6JO"},"agent_actions":{"view_html":"https://pith.science/pith/YB5NY6JO2ZFY4HKDPBTTWRKTVJ","download_json":"https://pith.science/pith/YB5NY6JO2ZFY4HKDPBTTWRKTVJ.json","view_paper":"https://pith.science/paper/YB5NY6JO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.0366&json=true","fetch_graph":"https://pith.science/api/pith-number/YB5NY6JO2ZFY4HKDPBTTWRKTVJ/graph.json","fetch_events":"https://pith.science/api/pith-number/YB5NY6JO2ZFY4HKDPBTTWRKTVJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YB5NY6JO2ZFY4HKDPBTTWRKTVJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YB5NY6JO2ZFY4HKDPBTTWRKTVJ/action/storage_attestation","attest_author":"https://pith.science/pith/YB5NY6JO2ZFY4HKDPBTTWRKTVJ/action/author_attestation","sign_citation":"https://pith.science/pith/YB5NY6JO2ZFY4HKDPBTTWRKTVJ/action/citation_signature","submit_replication":"https://pith.science/pith/YB5NY6JO2ZFY4HKDPBTTWRKTVJ/action/replication_record"}},"created_at":"2026-05-18T02:42:08.121208+00:00","updated_at":"2026-05-18T02:42:08.121208+00:00"}