{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ASWX2J4VC4LNOZUOQYVV5PQTRQ","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":"ca0e7ec96fed5511f80a984a2ac6190ead08a061ca0ad7255be10f79a7955f5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-11-16T05:34:33Z","title_canon_sha256":"ac030bde9d031cfdb007b5cce29aac4fbb7aca0835ef979d47c176388f641a26"},"schema_version":"1.0","source":{"id":"1711.05933","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.05933","created_at":"2026-05-18T00:11:18Z"},{"alias_kind":"arxiv_version","alias_value":"1711.05933v1","created_at":"2026-05-18T00:11:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05933","created_at":"2026-05-18T00:11:18Z"},{"alias_kind":"pith_short_12","alias_value":"ASWX2J4VC4LN","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"ASWX2J4VC4LNOZUO","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"ASWX2J4V","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:47156fd107c1cb9c65e7e65126676f99cd7d72abda2de91491685c275c374e06","target":"graph","created_at":"2026-05-18T00:11:18Z","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":"Let $G$ be a central product of two groups $H$ and $K$. We study second cohomology group of $G$, having coefficients in a divisible abelian group $D$ with trivial $G$-action, in terms of the second cohomology groups of certain quotients of $H$ and $K$. In particular, for $D = \\mathbb{C}^{*}$, some of our results provide a refinement of results from [Some groups with non-trivial multiplicators, Math. Z. {\\bf 120 } (1971), 307-308] and [On the Schur multiplicator of a central quotient of a direct product of groups, J. Pure Appl. Algebra {\\bf 3} (1973), 73-82].","authors_text":"L. R. Vermani, Manoj K. Yadav, Sumana Hatui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-11-16T05:34:33Z","title":"The Schur multiplier of central product of groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05933","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":"sha256:2b1c2367cc34adf0baa8483469cf11da5e90e680b4d289817feb8907cf37602e","target":"record","created_at":"2026-05-18T00:11:18Z","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":"ca0e7ec96fed5511f80a984a2ac6190ead08a061ca0ad7255be10f79a7955f5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-11-16T05:34:33Z","title_canon_sha256":"ac030bde9d031cfdb007b5cce29aac4fbb7aca0835ef979d47c176388f641a26"},"schema_version":"1.0","source":{"id":"1711.05933","kind":"arxiv","version":1}},"canonical_sha256":"04ad7d27951716d7668e862b5ebe138c01c68e90587d236aa70bde5c12e3922d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04ad7d27951716d7668e862b5ebe138c01c68e90587d236aa70bde5c12e3922d","first_computed_at":"2026-05-18T00:11:18.406391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:18.406391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4h2dRMSQDypbKP3Wz/05bau+FRmC50L9K/lWaRlFpsen7D0AgLo5A+T6S1I0XesN7mEaXN75mbrCp9TTFul+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:18.407050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.05933","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b1c2367cc34adf0baa8483469cf11da5e90e680b4d289817feb8907cf37602e","sha256:47156fd107c1cb9c65e7e65126676f99cd7d72abda2de91491685c275c374e06"],"state_sha256":"6ae0047d0bd6f762390f684a5fc7c78e1ef9a5cd450dbc6409469d110d862c66"}