{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6C7ZTJKLWKQKB3RNCPF6FJ6CJ3","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":"77c04cb5549c53cb2dc0ff01def3355b0f0b1768ef8a855efc471b98d47fdaee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-20T15:29:48Z","title_canon_sha256":"ba2294bfe5e351d565e440f12c40526c838d3248e45a191124f199ca72d701cc"},"schema_version":"1.0","source":{"id":"1303.4966","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4966","created_at":"2026-05-18T03:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4966v1","created_at":"2026-05-18T03:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4966","created_at":"2026-05-18T03:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"6C7ZTJKLWKQK","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6C7ZTJKLWKQKB3RN","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6C7ZTJKL","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:e2fc0ce81ad2687c3055800fe37275faf1b88267d5361984b724e222c96dde93","target":"graph","created_at":"2026-05-18T03:30:15Z","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":"An automorphism of a group G is called an IA-automorphism if it induces the identity automorphism on the abelianized group G/G'. Let IA(G) denote the group of all IA-automorphisms of G. We classify all finitely generated nilpotent groups G of class 2 for which IA(G) is isomorphic to Inn(G). In particular, we classify all finite nilpotent groups of class 2 for which each IA-automorphism is inner. As consequences, we give surprisingly very easy proofs of converse of Schur's theorem and also prove some other related results.","authors_text":"Deepak Gumber, Hemant Kalra, Sandeep Singh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-20T15:29:48Z","title":"Automorphisms of groups and converse of Schur's theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4966","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":"sha256:264fdc57b42b7505628605b27d787ee06fbf254c947aa1f494ecb79602e1db3d","target":"record","created_at":"2026-05-18T03:30:15Z","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":"77c04cb5549c53cb2dc0ff01def3355b0f0b1768ef8a855efc471b98d47fdaee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-20T15:29:48Z","title_canon_sha256":"ba2294bfe5e351d565e440f12c40526c838d3248e45a191124f199ca72d701cc"},"schema_version":"1.0","source":{"id":"1303.4966","kind":"arxiv","version":1}},"canonical_sha256":"f0bf99a54bb2a0a0ee2d13cbe2a7c24ec692de3a6a8678bd8ef7b288aa9d9467","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0bf99a54bb2a0a0ee2d13cbe2a7c24ec692de3a6a8678bd8ef7b288aa9d9467","first_computed_at":"2026-05-18T03:30:15.531652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:15.531652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lkrlOF5t+xF4wYa/MxSiBWKG5xUNuYFFG0LclXIhqBq8A2dtvWJSBdl5kSizGdlhdi66D+k1cVHDSsnm/Q/IAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:15.532417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4966","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:264fdc57b42b7505628605b27d787ee06fbf254c947aa1f494ecb79602e1db3d","sha256:e2fc0ce81ad2687c3055800fe37275faf1b88267d5361984b724e222c96dde93"],"state_sha256":"e6c2846a49209b196381dabb2af31fc02174ac112029e48f2d71942950f04a3c"}