{"paper":{"title":"On Normal Subgroups 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":"2025-02-07T08:58:10Z","abstract_excerpt":"In this paper, we prove two structure theorems for twisted Chevalley groups $G_\\sigma (R)$ over a commutative ring $R$ with unity. The first theorem concerns the normality of $E'_\\sigma (R,J)$, the elementary congruence subgroups at level $J$, in the group $G_\\sigma (R)$. The second theorem classifies all subgroups of $G_\\sigma (R)$ normalized by its elementary subgroup $E'_\\sigma (R)$. Along the way, we obtain several interesting results. For instance, when $R$ is a semilocal ring, we show that $G_\\sigma(R)$ can be expressed as the (internal) product of $E'_\\sigma (R)$ and the maximal torus $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.04766","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.04766/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"}