{"paper":{"title":"Zassenhaus Conjecture on torsion units holds for $\\text{SL}(2,p)$ and $\\text{SL}(2,p^2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"\\'Angel del R\\'io, Mariano Serrano","submitted_at":"2018-03-14T15:09:40Z","abstract_excerpt":"H.J. Zassenhaus conjectured that any unit of finite order and augmentation $1$ in the integral group ring $\\mathbb{Z}G$ of a finite group $G$ is conjugate in the rational group algebra $\\mathbb{Q}G$ to an element of $G$. We prove the Zassenhaus Conjecture for the groups $\\text{SL}(2,p)$ and $\\text{SL}(2,p^2)$ with $p$ a prime number. This is the first infinite family of non-solvable groups for which the Zassenhaus Conjecture has been proved. We also prove that if $G=\\text{SL}(2,p^f)$, with $f$ arbitrary and $u$ is a torsion unit of $\\mathbb{Z}G$ with augmentation $1$ and order coprime with $p$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05342","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"}