{"paper":{"title":"On torsion units in integral group rings of Frobenius groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Martin Hertweck","submitted_at":"2012-07-22T20:10:18Z","abstract_excerpt":"For a finite group $G$, let $\\tilde{\\mathbb{Z}}$ be the semilocalization of $\\mathbb{Z}$ at the prime divisors of $|G|$. If $G$ is a Frobenius group with Frobenius kernel $K$, it is shown that each torsion unit in the group ring $\\tilde{\\mathbb{Z}} G$ which maps to the identity under the natural ring homomorphism $\\tilde{\\mathbb{Z}} G \\rightarrow \\tilde{\\mathbb{Z}} G/K$ is conjugate to an element of $G$ by a unit in $\\tilde{\\mathbb{Z}} G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5256","kind":"arxiv","version":1},"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"}