{"paper":{"title":"Kernel of Scott modules and Brauer indecomposability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The kernel of a Scott kG-module determines its Brauer indecomposability via a generalized criterion, and this property lifts from p-local subgroups in certain cases.","cross_cats":[],"primary_cat":"math.RT","authors_text":"Lin Wu","submitted_at":"2026-05-07T06:53:03Z","abstract_excerpt":"Let $k$ be an algebraically closed field of a prime characteristic $p$. Let $G$ be a finite group. We investigate the Brauer indecomposability of Scott $kG$-modules in relation to the kernel of modules. We generalize a criterion for Brauer indecomposability. We also prove that, in certain cases, Brauer indecomposability of a Scott $kG$-module can be lifted from that of a Scott module over a $p$-local subgroup."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We generalize a criterion for Brauer indecomposability. We also prove that, in certain cases, Brauer indecomposability of a Scott kG-module can be lifted from that of a Scott module over a p-local subgroup.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The lifting holds only 'in certain cases' whose precise hypotheses are not stated in the abstract; the criterion generalization likewise depends on unspecified conditions on the kernel or on the group structure.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The work generalizes a criterion for Brauer indecomposability of Scott kG-modules and establishes lifting of this property from p-local subgroups in specified cases.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The kernel of a Scott kG-module determines its Brauer indecomposability via a generalized criterion, and this property lifts from p-local subgroups in certain cases.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fc596997def028230f828e580ee6400ddccaf7cbcb21cffde28bd1a39fead28a"},"source":{"id":"2605.05757","kind":"arxiv","version":2},"verdict":{"id":"0cbe2f4c-97d8-4b8e-8e25-092028b1747b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T04:13:07.437696Z","strongest_claim":"We generalize a criterion for Brauer indecomposability. We also prove that, in certain cases, Brauer indecomposability of a Scott kG-module can be lifted from that of a Scott module over a p-local subgroup.","one_line_summary":"The work generalizes a criterion for Brauer indecomposability of Scott kG-modules and establishes lifting of this property from p-local subgroups in specified cases.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The lifting holds only 'in certain cases' whose precise hypotheses are not stated in the abstract; the criterion generalization likewise depends on unspecified conditions on the kernel or on the group structure.","pith_extraction_headline":"The kernel of a Scott kG-module determines its Brauer indecomposability via a generalized criterion, and this property lifts from p-local subgroups in certain cases."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.05757/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T20:01:19.504821Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T13:18:00.830664Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"dbf3ece2f6a7ef302c0640558c2093b7a6ddaa109de8e55407dd263804d17d21"},"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"}