{"paper":{"title":"Overgroups of subsystem subgroups in exceptional groups: inside a sandwich","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Pavel Gvozdevsky","submitted_at":"2021-07-02T19:49:27Z","abstract_excerpt":"The current paper is an addition to the previous paper by author, where the overgroup lattice of the elementary subsystem subgroup $E(\\Delta,R)$ of the Chevalley group $G(\\Phi,R)$ for a large enough root subsystem $\\Delta$ was studied. Now we study the connection between the elementary subgroup $\\hat{E}(\\sigma)$ given by the net of ideals of the ring $R$ and the stabilizer $S(\\sigma)$ of the corresponding Lie subalgebra of the Chevalley algebra. In particular, we prove that under a certain condition the subgroup $\\hat{E}(\\sigma)$ is normal in $S(\\sigma)$, and we also study some properties of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.01249","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/2107.01249/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"}