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Then using a result of M.R.R.Moghaddam [6], we will be able to deduce a result of Schur's type (see [4,9]) with respect to the variety of nilpotent groups of class at most $c$ $(c\\geq 1)$, when $c+1$ is any prime number or 4."},"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":"1104.0398","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-04-03T16:04:02Z","cross_cats_sorted":[],"title_canon_sha256":"43efe793299884b741b6e3c105a81be76dfa54c399db2f3bf7caf07d1da8ab79","abstract_canon_sha256":"a9debbe6c403380e2643ab7ed2ab58b383d5241909e0ca15f1728be3dcd08c6c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:04.100954Z","signature_b64":"Lz2w9fVyzzRxXlgfoBVZqM1NyAlVGagO/aoKqw09TsNPqUUGbqv6lMbhx5c4l/GwWubCGjBxtIRYRecbphLMCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90ad35db69dbf79accf84c8da0ac20edc952c119bda2011e7d33b3c260413b51","last_reissued_at":"2026-05-18T04:25:04.100545Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:04.100545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subgroup Theorems for the Baer-invariant of Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Behrooz Mashayekhy, Mohammad Reza Rajabzadeh Moghaddam, Saeed Kayvanfar","submitted_at":"2011-04-03T16:04:02Z","abstract_excerpt":"M.R.Jones and J.Wiegold in [3] have shown that if $G$ is a finite group with a subgroup $H$ of finite index $n$, then the $n$-th power of Schur multiplier of $G$, $M(G)^n$, is isomorphic to a subgroup of $M(H)$.\n  In this paper we prove a similar result for the centre by centre by $w$ variety of groups, where $w$ is any outer commutator word. 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