{"paper":{"title":"Overgroups of subsystem subgroups in exceptional groups: 2A1-proof","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Pavel Gvozdevsky","submitted_at":"2019-10-17T16:31:16Z","abstract_excerpt":"In the present paper we prove a weak form of sandwich classification for the overgroups of the subsystem subgroup $E(\\Delta,R)$ of the Chevalley group $G(\\Phi,R)$ where $\\Phi$ is a simply laced root sysetem and $\\Delta$ is its sufficiently large subsystem. Namely we show that for any such an overgroup $H$ there exists a unique net of ideals $\\sigma$ of the ring $R$ such that $E(\\Phi,\\Delta,R,\\sigma)\\le H\\le {\\mathop{\\mathrm{Stab}}\\nolimits}_{G(\\Phi,R)}(L(\\sigma))$ where $E(\\Phi,\\Delta,R,\\sigma)$ is an elementary subgroup associated with the net and $L(\\sigma)$ is a corresponding subalgebra of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.08011","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/1910.08011/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"}