{"paper":{"title":"Group rings of finite strongly monomial groups: central units and primitive idempotents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"\\'Angel del R\\'io, Eric Jespers, Gabriela Olteanu, Inneke Van Gelder","submitted_at":"2012-09-06T12:42:37Z","abstract_excerpt":"We compute the rank of the group of central units in the integral group ring $\\Z G$ of a finite strongly monomial group $G$. The formula obtained is in terms of the strong Shoda pairs of $G$. Next we construct a virtual basis of the group of central units of $\\Z G$ for a class of groups $G$ properly contained in the finite strongly monomial groups. Furthermore, for another class of groups $G$ inside the finite strongly monomial groups, we give an explicit construction of a complete set of orthogonal primitive idempotents of $\\Q G$.\n  Finally, we apply these results to describe finitely many ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1269","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"}