{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EVAZ2UGODPJG47I4BSYSVIDVMB","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":"68291d9f4da1800a0a478d816d43b38864c2f871c9d7c99d7f3c81ba8cc60426","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-29T08:39:50Z","title_canon_sha256":"531a4f2ba830bd484bd2c6108d304a539d85b1d19eef3c728b0a19c85958b709"},"schema_version":"1.0","source":{"id":"1301.6865","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6865","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6865v1","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6865","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"pith_short_12","alias_value":"EVAZ2UGODPJG","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EVAZ2UGODPJG47I4","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EVAZ2UGO","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:3d6a90ce4e5332e083d1c311b8251be841513386f5ebb372549d684148147c9f","target":"graph","created_at":"2026-05-18T01:35:57Z","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. A subgroup $H$ of $G$ is said to be weakly S-embedded in $G$ if there exists $K\\unlhd G$ such that $HK$ is S-quasinormal in $G$ and $H\\cap K\\leq H_{seG}$, where $H_{seG}$ is the subgroup generated by all those subgroups of $H$ which are S-quasinormally embedded in $G$. We say that $H$ is weakly $\\tau$-embedded in $G$ if there exists $K\\unlhd G$ such that $HK$ is S-quasinormal in $G$ and $H\\cap K\\leq H_{\\tau G}$, where $H_{\\tau G}$ is the subgroup generated by all those subgroups of $H$ which are $\\tau$-quasinormal in $G$. In this paper, we study the properties of the","authors_text":"Wenbin Guo, Xiaoyu Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-29T08:39:50Z","title":"On weakly S-embedded subgroups and weakly $\\tau$-embedded subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6865","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:b43cb7bb276b45289371f94f15382d187f121b44edc3347d86f9f307dee11208","target":"record","created_at":"2026-05-18T01:35:57Z","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":"68291d9f4da1800a0a478d816d43b38864c2f871c9d7c99d7f3c81ba8cc60426","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-29T08:39:50Z","title_canon_sha256":"531a4f2ba830bd484bd2c6108d304a539d85b1d19eef3c728b0a19c85958b709"},"schema_version":"1.0","source":{"id":"1301.6865","kind":"arxiv","version":1}},"canonical_sha256":"25419d50ce1bd26e7d1c0cb12aa075605bf279d4a577bf0ea3bd7404c653efe6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25419d50ce1bd26e7d1c0cb12aa075605bf279d4a577bf0ea3bd7404c653efe6","first_computed_at":"2026-05-18T01:35:57.643585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:57.643585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1PIcIF7SWs6xLJxnX4s1JX0Lo0kj3u1OQbJi3En7Zb4Ck651TxFOW1snoSvstpgLGCGzv8IA0fsZnjkeqNLCDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:57.644087Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.6865","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b43cb7bb276b45289371f94f15382d187f121b44edc3347d86f9f307dee11208","sha256:3d6a90ce4e5332e083d1c311b8251be841513386f5ebb372549d684148147c9f"],"state_sha256":"3ba2f6ce71fbd081ca8dc8b76506350fed1561d3aa8d78b6e60635c9a79b62de"}