{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZKINLQELKEMXY66CCEX7IO2FDO","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":"5fe7cc3ac32c94ff493128b72103fe0a0d49e583af39487e99f08c3d07be6236","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-02T05:00:47Z","title_canon_sha256":"a928600cc42834bc54b2c535d51d2dc41e154865e073afa0772ff95856324e7b"},"schema_version":"1.0","source":{"id":"1308.0408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0408","created_at":"2026-05-18T03:16:50Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0408v1","created_at":"2026-05-18T03:16:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0408","created_at":"2026-05-18T03:16:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZKINLQELKEMX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZKINLQELKEMXY66C","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZKINLQEL","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:13f0ce4bc1fc158cdf0efda4373a606072dc0345e253435c9259c80026846042","target":"graph","created_at":"2026-05-18T03:16:50Z","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 $H$ be a subgroup of a group $G$. $H$ is said satisfying $\\Pi$-property in $G$, if $|G/K:N_{G/K}(HK/K\\cap L/K)|$ is a\n  $\\pi(HK/K\\cap L/K))$-number for any chief factor $L/K$ of $G$, and, if there is a subnormal supplement $T$ of $H$ in $G$ such that $H\\cap T\\le I\\le H$ for some subgroup $I$ satisfying $\\Pi$-property in $G$, then $H$ is said $\\Pi$-normal in $G$. By these properties of some subgroups, we obtain some new criterions of $p$-nilpotency of finite groups.","authors_text":"Baojun LI, Tuval Foguel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-02T05:00:47Z","title":"On p-nilpotency of finite groups?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0408","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:a704d843b1b057fdf49170716a1525bf32d2689d74314f54144d93ffc8223162","target":"record","created_at":"2026-05-18T03:16:50Z","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":"5fe7cc3ac32c94ff493128b72103fe0a0d49e583af39487e99f08c3d07be6236","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-02T05:00:47Z","title_canon_sha256":"a928600cc42834bc54b2c535d51d2dc41e154865e073afa0772ff95856324e7b"},"schema_version":"1.0","source":{"id":"1308.0408","kind":"arxiv","version":1}},"canonical_sha256":"ca90d5c08b51197c7bc2112ff43b451b874380b215e2fb1fa267afeaba948297","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca90d5c08b51197c7bc2112ff43b451b874380b215e2fb1fa267afeaba948297","first_computed_at":"2026-05-18T03:16:50.537498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:50.537498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x6VTMYFKz4MJrlbxnP3Ma0HpZ499bjj1n4KFtp3FJNBkuN0UDOtNuqGIv4i4iiwlvLTTW/OOM/eA9/3hXV6/DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:50.538145Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a704d843b1b057fdf49170716a1525bf32d2689d74314f54144d93ffc8223162","sha256:13f0ce4bc1fc158cdf0efda4373a606072dc0345e253435c9259c80026846042"],"state_sha256":"da0917ee4e43b0d11693b70c6d4c7146c48bcaf8c81d6f30eca3f4acd88f04e5"}