{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AFYO4MTDW6ICNUYZDBCBTBYTAD","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":"884f9bf7e9bca5c86ce89f50aa91363e3fcb8eedf4311b9a87e3eec93188523f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-18T16:27:43Z","title_canon_sha256":"d80ce2519ba7f232a9079940fab2cbebe24583db2a404244c60ba75f9b9b52dc"},"schema_version":"1.0","source":{"id":"1701.05134","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05134","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05134v1","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05134","created_at":"2026-05-18T00:52:33Z"},{"alias_kind":"pith_short_12","alias_value":"AFYO4MTDW6IC","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AFYO4MTDW6ICNUYZ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AFYO4MTD","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:13075f8ddd0a4e6d7a0a986adfa7d9d33fa8bebab5fe97d63715cab706f8a3b0","target":"graph","created_at":"2026-05-18T00:52:33Z","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 finite group. Let $\\sigma =\\{\\sigma_{i} | i\\in I\\}$ be a partition of the set of all primes $\\Bbb{P}$ and $n$ an integer. We write $\\sigma (n) =\\{\\sigma_{i} |\\sigma_{i}\\cap \\pi (n)\\ne \\emptyset \\}$, $\\sigma (G) =\\sigma (|G|)$. A set $ {\\cal H}$ of subgroups of $G$ is said to be a complete Hall $\\sigma $-set of $G$ if every member of ${\\cal H}\\setminus \\{1\\}$ is a Hall $\\sigma_{i}$-subgroup of $G$ for some $\\sigma_{i}$ and ${\\cal H}$ contains exact one Hall $\\sigma_{i}$-subgroup of $G$ for every $\\sigma_{i}\\in \\sigma (G)$. A subgroup $A$ of $G$ is called: (i) a $\\sigma$-Hall subgro","authors_text":"Alexander N. Skiba, Chi Zhang, Darya A. Sinitsa, Wenbin Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-18T16:27:43Z","title":"On $H_{\\sigma}$-permutably embedded and $H_{\\sigma}$-subnormaly embedded subgroups of finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05134","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":"sha256:015e82621f74aaa14ac719af874936c669a91e6089c41e3b2d8456d28e25237c","target":"record","created_at":"2026-05-18T00:52:33Z","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":"884f9bf7e9bca5c86ce89f50aa91363e3fcb8eedf4311b9a87e3eec93188523f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-18T16:27:43Z","title_canon_sha256":"d80ce2519ba7f232a9079940fab2cbebe24583db2a404244c60ba75f9b9b52dc"},"schema_version":"1.0","source":{"id":"1701.05134","kind":"arxiv","version":1}},"canonical_sha256":"0170ee3263b79026d319184419871300c8c8d826e994bbd50d7d26556d612c12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0170ee3263b79026d319184419871300c8c8d826e994bbd50d7d26556d612c12","first_computed_at":"2026-05-18T00:52:33.118248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:33.118248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OjMavh6t5OURLAwIrWE6dw80hnOxJBD8L0L5KGCH4NJpqry7xtelwmKpbIhOFrSegaZaDtIi64GsNC5GbvNkDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:33.118803Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05134","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:015e82621f74aaa14ac719af874936c669a91e6089c41e3b2d8456d28e25237c","sha256:13075f8ddd0a4e6d7a0a986adfa7d9d33fa8bebab5fe97d63715cab706f8a3b0"],"state_sha256":"f37761ad3f9d1d328a3008d31ac4c8a0bab0d1a58dfc3eda33e2f764d689b594"}