{"paper":{"title":"Normalizer of Twisted Chevalley Groups over Commutative Rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Deep H. Makadiya, Shripad M. Garge","submitted_at":"2025-03-21T06:56:39Z","abstract_excerpt":"Let $R$ be a commutative ring with unity. Consider the twisted Chevalley group $G_{\\pi, \\sigma} (\\Phi, R)$ of type $\\phi$ over $R$ and its elementary subgroup $E'_{\\pi, \\sigma} (\\Phi, R)$. This paper investigates the normalizers of $E'_{\\pi, \\sigma}(\\Phi, R)$ and $G_{\\pi, \\sigma}(\\Phi, R)$ in the larger group $G_{\\pi, \\sigma}(\\Phi, S)$, where $S$ is an extension ring of $R$. We establish that under certain conditions on $R$ these normalizers coincide. Moreover, in the case of adjoint type groups, we show that they are precisely equal to $G_{\\pi, \\sigma}(\\Phi, R)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.16894","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.16894/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}