{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DPMEEJTNLA2OIOAIUTM2UL52OW","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":"81085b3e0eeaaaf203440c524638b765278aacbe4fd4a76470cc3d06382a36f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-30T07:09:02Z","title_canon_sha256":"29aca0c40a183324fb115b15c473589d9bff36903380f82f1e3416869db2af2f"},"schema_version":"1.0","source":{"id":"1705.10476","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10476","created_at":"2026-05-18T00:43:24Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10476v1","created_at":"2026-05-18T00:43:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10476","created_at":"2026-05-18T00:43:24Z"},{"alias_kind":"pith_short_12","alias_value":"DPMEEJTNLA2O","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DPMEEJTNLA2OIOAI","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DPMEEJTN","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:f3174b49c2a2f47a2e035cd271626769d7587b585fae52e576c7b30f1d09a127","target":"graph","created_at":"2026-05-18T00:43:24Z","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 $\\frak {F}$ be a class of group. A subgroup $A$ of a finite group $G$ is said to be $K$-$\\mathfrak{F}$-subnormal in $G$ if there is a subgroup chain $$A=A_{0} \\leq A_{1} \\leq \\cdots \\leq A_{n}=G$$ such that either $A_{i-1} \\trianglelefteq A_{i}$ or $A_{i}/(A_{i-1})_{A_{i}} \\in \\mathfrak{F}$ for all $i=1, \\ldots , n$. A formation $\\frak {F}$ is said to be $K$-lattice provided in every finite group $G$ the set of all its $K$-$\\mathfrak{F}$-subnormal subgroups forms a sublattice of the lattice of all subgroups of $G$.\n  In this paper we consider some new applications of the theory of $K$-latt","authors_text":"Alexander N. Skiba, Vladimir N. Semenchuk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-30T07:09:02Z","title":"Finite groups with systems of $K$-$\\frak{F}$-subnormal subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10476","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":"sha256:4c62b56126120060af0ba13553ea1c2bf33ec6d2b4e9aa548bfe615b7663cd45","target":"record","created_at":"2026-05-18T00:43:24Z","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":"81085b3e0eeaaaf203440c524638b765278aacbe4fd4a76470cc3d06382a36f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-30T07:09:02Z","title_canon_sha256":"29aca0c40a183324fb115b15c473589d9bff36903380f82f1e3416869db2af2f"},"schema_version":"1.0","source":{"id":"1705.10476","kind":"arxiv","version":1}},"canonical_sha256":"1bd842266d5834e43808a4d9aa2fba75ba481a09c406d0c3e413b09af5ab495b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bd842266d5834e43808a4d9aa2fba75ba481a09c406d0c3e413b09af5ab495b","first_computed_at":"2026-05-18T00:43:24.476230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:24.476230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"42WmyaeF72lyC/R6gDrQ/J/xKMQIHMI2RizBcQ5zSauiL/HUlAcYGonFniYrlEJUAlKV36SJ4H/nnQx92P9DBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:24.476798Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.10476","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c62b56126120060af0ba13553ea1c2bf33ec6d2b4e9aa548bfe615b7663cd45","sha256:f3174b49c2a2f47a2e035cd271626769d7587b585fae52e576c7b30f1d09a127"],"state_sha256":"6ef6a93b2ff71342bba1e1ba97281f3ec4f3fd0395cc6fff76b9ee81797fb4fb"}