{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TKCRGFJRN4J6EZAQD557Z45PKP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f4b2c48dee6f2ddaf913ecfbf11894614f7f776e630b38c08151337149351748","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-23T21:38:35Z","title_canon_sha256":"6edb9d9fead276665f5adc240ced6e34d50be338e0bbda8ba65a3db93d3a2e19"},"schema_version":"1.0","source":{"id":"1311.6056","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6056","created_at":"2026-05-18T03:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6056v1","created_at":"2026-05-18T03:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6056","created_at":"2026-05-18T03:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"TKCRGFJRN4J6","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TKCRGFJRN4J6EZAQ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TKCRGFJR","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:790f0aeb37dbd5efe75ff4e4e386152d5dd6dd1cbf7adaa89785dc2bdeab90d9","target":"graph","created_at":"2026-05-18T03:06:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In [Li and Chen, A new characterization of the simple group A_1(p^n), Sib. Math. J., 2012], it is proved that the simple group A_1(p^n) is uniquely determined by the set of orders of its maximal abelian subgroups. Also in [Momen and Khosravi, Groups with the same orders of maximal abelian subgroups as A_2(q), Monatsh. Math., 2013], the authors proved that if L=A_2(q), where q is not a Mersenne prime, then every finite group with the same orders of maximal abelian subgroups as L, is isomorphic to L or an extension of L by a subgroup of the outer automorphism group of L. In this paper, we prove ","authors_text":"Behrooz Khosravi, Zahra Momen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-23T21:38:35Z","title":"On recognizability of PSU_3(q) by the orders of maximal abelian subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6056","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:087c8b4e1efc5ad91b99d9da593aec28c2eee59e84c8ad8feba45383c5ee29cb","target":"record","created_at":"2026-05-18T03:06:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f4b2c48dee6f2ddaf913ecfbf11894614f7f776e630b38c08151337149351748","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-23T21:38:35Z","title_canon_sha256":"6edb9d9fead276665f5adc240ced6e34d50be338e0bbda8ba65a3db93d3a2e19"},"schema_version":"1.0","source":{"id":"1311.6056","kind":"arxiv","version":1}},"canonical_sha256":"9a851315316f13e264101f7bfcf3af53f5c390a4f63c5da6de93575ca99f57f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a851315316f13e264101f7bfcf3af53f5c390a4f63c5da6de93575ca99f57f1","first_computed_at":"2026-05-18T03:06:20.670065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:20.670065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ERMhurP/rV8N/70Z2S5JeS6OuNBGFNw7QWulKh8Hc72faFOx7VLuS6QQGhDkegDVQrH0QuMl2PUCQFmG2VAbDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:20.670633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6056","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:087c8b4e1efc5ad91b99d9da593aec28c2eee59e84c8ad8feba45383c5ee29cb","sha256:790f0aeb37dbd5efe75ff4e4e386152d5dd6dd1cbf7adaa89785dc2bdeab90d9"],"state_sha256":"57bac376937ea42c15b09b2157ae897de0aeb09c0f2e4a442a9f2a4e0ca0072f"}