{"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. Bakshi, Sugandha Maheshwary","submitted_at":"2014-08-19T11:03:40Z","abstract_excerpt":"Let $\\mathcal{Z}(\\mathcal{U}(\\mathbb{Z}[G]))$ denote the group of central units in the integral group ring $\\mathbb{Z}[G]$ of a finite group $G$. 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4293","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}