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A cover $\\Pi =\\{H_1, H_2, \\dots, H_n\\}$ is said to be a  strict $\\mathit{S}$-partition of $G$ if $H_i\\cap H_j= S$ for $i\\neq j$ and $\\Pi$ is said an equal strict $\\mathit{S}$-partition (or $ES$-partition ) of $G$, if $\\Pi$ is a strict $S$-partition and $|H_i|=|H_j|$ for all $i\\neq j$. If $S$ is the identity subgroup and $G$ has a strict $S$-partition (equal strict $\\mathit{S}$-partition), then we say that $G$ has a partit"},"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":"1804.06684","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-04-18T12:33:33Z","cross_cats_sorted":[],"title_canon_sha256":"3cd90efb48746bba26aff315681af19b3802c7bb295d3de9cc8817047f59607b","abstract_canon_sha256":"2ffeb6f2691904a3970f4d0f83e43ec65c98209ea47a29563e3b49b407dcca44"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:06.016857Z","signature_b64":"Lgqz7RoL34niJ244nlwS2tdToM8aNsRTuWkDewAceILJFbh5R//wHCrjF4qDImMREoDfFIwXLbJsqwepTCPhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc7aed71ee8a97008c53aba51098f1803b8e30e8d9e09bf96220e27f9b1b2134","last_reissued_at":"2026-05-18T00:18:06.016026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:06.016026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Criteria for nilpotency of groups via partitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"L.J. 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