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A bound on the index of the subgroup generated by a virtual basis in $\\mathcal{Z}(\\mathcal{U}(\\mathbb{Z}[G]))$ is computed for a class of strongly monomial groups. The result is illustrated with application to the groups of order $p^{n}$, $p$ prime, $n \\leq 4$. The rank of $\\mathcal{Z}(\\mathcal{U}(\\mathbb{Z}[G]))$ and the Wedderburn decomposition of the rational group algebra of these $p$-groups have also been obtained."},"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":"1408.4293","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-08-19T11:03:40Z","cross_cats_sorted":[],"title_canon_sha256":"8dd0b1652e95bf1a063be3a299fba98f7aa1e1b6d50ca25c716ef88eaefda1da","abstract_canon_sha256":"82c7f10dd90cc8edf242a7171dd17d093879faf6ca65e41675514384f8f72ec8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:51.035935Z","signature_b64":"5pSWbefgn7BT0ie8ewZxXejx/fu5V4OYAklgZe4F4cAw76qfpApt7e+vcOZoqJQ4vBKYEp/dIQxD+1EHvYtgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d753f8ec1f5d0bff214a2a372366475c94cddb4b4819cb3a26ff0fb0a97b456","last_reissued_at":"2026-05-18T00:12:51.035436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:51.035436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the index of a free abelian subgroup in the group of central units of an integral group ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Gurmeet K. 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