{"paper":{"title":"Simple groups with narrow prime spectrum: Extended list","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"All non-abelian finite simple groups whose order has largest prime divisor at most 10000 have been determined.","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrei V. Zavarnitsine","submitted_at":"2026-05-15T03:18:13Z","abstract_excerpt":"Generalising a previous result, we determine all non-abelian finite simple groups whose order has largest prime divisor not exceeding $10^4$. The computer code for this and similar calculations is made available."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We determine all non-abelian finite simple groups whose order has largest prime divisor not exceeding 10^4.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The classification of finite simple groups is complete and the orders of all known simple groups are correctly tabulated in the literature or databases used by the program.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"All non-abelian finite simple groups with largest prime divisor at most 10^4 are listed via exhaustive computational search over the known simple groups.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"All non-abelian finite simple groups whose order has largest prime divisor at most 10000 have been determined.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2b8f046e0694f463afc75126ef9fd1286f72a1d74ead309c675ccc7e4759ecfa"},"source":{"id":"2605.16450","kind":"arxiv","version":1},"verdict":{"id":"090ff5b7-a67f-4bda-88ff-bc8d3e4f6a91","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T21:52:51.046430Z","strongest_claim":"We determine all non-abelian finite simple groups whose order has largest prime divisor not exceeding 10^4.","one_line_summary":"All non-abelian finite simple groups with largest prime divisor at most 10^4 are listed via exhaustive computational search over the known simple groups.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The classification of finite simple groups is complete and the orders of all known simple groups are correctly tabulated in the literature or databases used by the program.","pith_extraction_headline":"All non-abelian finite simple groups whose order has largest prime divisor at most 10000 have been determined."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16450/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T22:01:30.345419Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T22:01:23.305927Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:34:35.256001Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:21:57.082109Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"7aeb7d315c56a6e14e5c45ffb0daddc9211b876b2c14c24e0196c43f8f6b2144"},"references":{"count":5,"sample":[{"doi":"","year":1985,"title":"J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wil- son, Atlas of finite groups: maximal subgroups and ordinary characters for simple groups. Oxford. Clarendon Press (1985), xxxiii + 25","work_id":"73134111-3643-4078-a332-9e496b803c34","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"URL: http://www.gap-system.org","work_id":"fc5f597f-b150-41a2-a544-6a632ae2a919","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1994,"title":"V. D. Mazurov, On the set of orders of elements of a finite group, Algebra and Logic,33, N 1 (1994), 49–55","work_id":"0fb07358-1796-4e01-b634-4fd30730e2e7","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"A. V. Zavarnitsine, Finite simple groups with narrow prime spectrum,Sib. Elect. Math. Reports,6(2009), 1–12. 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