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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.6865","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-29T08:39:50Z","cross_cats_sorted":[],"title_canon_sha256":"531a4f2ba830bd484bd2c6108d304a539d85b1d19eef3c728b0a19c85958b709","abstract_canon_sha256":"68291d9f4da1800a0a478d816d43b38864c2f871c9d7c99d7f3c81ba8cc60426"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:57.644087Z","signature_b64":"1PIcIF7SWs6xLJxnX4s1JX0Lo0kj3u1OQbJi3En7Zb4Ck651TxFOW1snoSvstpgLGCGzv8IA0fsZnjkeqNLCDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25419d50ce1bd26e7d1c0cb12aa075605bf279d4a577bf0ea3bd7404c653efe6","last_reissued_at":"2026-05-18T01:35:57.643585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:57.643585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On weakly S-embedded subgroups and weakly $\\tau$-embedded subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Wenbin Guo, Xiaoyu Chen","submitted_at":"2013-01-29T08:39:50Z","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 $G$. 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