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In 2009, Niroomand, improving Green's and other bounds on $|M(G)|$ for a non-abelain $p$-group $G$, proved that $|M(G)| \\leq p^{\\frac{1}{2}(n-k-1)(n+k-2)+1}$. In this article we note that a bound, obtained earlier, by Ellis and Weigold is more general than the bound of Niroomand. We derive from the bound of Ellis and Weigold that $|M(G)| \\leq p^{\\frac{1}{2}(d(G)-1)(n+k-2)+1}$ for a non-abelain $p$-group $G$."},"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":"1606.01493","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-05T11:23:01Z","cross_cats_sorted":[],"title_canon_sha256":"a7467e22cb7b8a957d18fbd162fb3743776b1357a696a2cc194d03d5fda8caf1","abstract_canon_sha256":"9fa1dd5dd66efa6416182134ba8613988a10a652ea7d901d5948ace2220341ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:54.046949Z","signature_b64":"j9d6p59ZbsCbRDjb7INI7lyey5xu2DVVi8mSpfMh7cuopVgXw+1eE3JvCSfpS8YBzjCQOGn30e4jhjItQ7bsAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5128fa8bd2a037beed990c8856a344ec20581da1a72818901f2aebe5be0b9a13","last_reissued_at":"2026-05-18T01:12:54.046573Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:54.046573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the order of the Schur multiplier of p-groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Pradeep K. Rai","submitted_at":"2016-06-05T11:23:01Z","abstract_excerpt":"Let $G$ be a finite $p$-group of order $p^n$ with $|G'| = p^k$. Let $M(G)$ denotes the Schur multiplier of $G$. A classical result of Green states that $|M(G)| \\leq p^{\\frac{1}{2}n(n-1)}$. In 2009, Niroomand, improving Green's and other bounds on $|M(G)|$ for a non-abelain $p$-group $G$, proved that $|M(G)| \\leq p^{\\frac{1}{2}(n-k-1)(n+k-2)+1}$. In this article we note that a bound, obtained earlier, by Ellis and Weigold is more general than the bound of Niroomand. 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