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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"},"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":"1701.05134","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-18T16:27:43Z","cross_cats_sorted":[],"title_canon_sha256":"d80ce2519ba7f232a9079940fab2cbebe24583db2a404244c60ba75f9b9b52dc","abstract_canon_sha256":"884f9bf7e9bca5c86ce89f50aa91363e3fcb8eedf4311b9a87e3eec93188523f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:33.118803Z","signature_b64":"OjMavh6t5OURLAwIrWE6dw80hnOxJBD8L0L5KGCH4NJpqry7xtelwmKpbIhOFrSegaZaDtIi64GsNC5GbvNkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0170ee3263b79026d319184419871300c8c8d826e994bbd50d7d26556d612c12","last_reissued_at":"2026-05-18T00:52:33.118248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:33.118248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $H_{\\sigma}$-permutably embedded and $H_{\\sigma}$-subnormaly embedded subgroups of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander N. Skiba, Chi Zhang, Darya A. Sinitsa, Wenbin Guo","submitted_at":"2017-01-18T16:27:43Z","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 $\\sigma_{i}\\in \\sigma (G)$. 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