{"paper":{"title":"Classification of abelian Schur groups II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Grigory Ryabov","submitted_at":"2026-05-18T13:12:18Z","abstract_excerpt":"A finite group $G$ is called a Schur group if every Schur ring over $G$ is schurian, i.e. associated in a natural way with a subgroup of the symmetric group $Sym(G)$ that contains all right translations of $G$. The list of all possible abelian Schur groups was obtained by Evdokimov, Kov\\'acs, and Ponomarenko in 2016. In two papers, we complete a classification of abelian Schur groups. In the present paper, we prove that several groups of nonpowerful order from the list are Schur groups. By that, we obtain a classification of abelian Schur groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18356","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18356/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:31.330516Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"external_links","ran_at":"2026-05-19T23:31:54.128219Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T23:21:58.800049Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"389a579886ff5b0cbfc2401058f7a57fe3e15961fd92d76c71925eb004ecb67c"},"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"}