{"paper":{"title":"A new look at the decomposition of unipotents and the normal structure of Chevalley groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Alexei Stepanov","submitted_at":"2015-12-08T01:25:59Z","abstract_excerpt":"The current article continues a series of papers on decomposition of unipotents and its applications. Let $G(\\Phi,R)$ be a Chevalley group with a reduced irreducible root system $\\Phi$ over a commutative ring $R$. Fix $h\\in G(\\Phi,R)$. Call an element $a\\in G(\\Phi,R)$ \"good\", if it lies in the unipotent radical of a parabolic subgroup whereas the conjugate to $a$ by $h$ belongs to another proper parabolic subgroup (here we assume that all parabolics contain a given split maximal torus). Decomposition of unipotents is a representation of a root unipotent element as a product of \"good\" elements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02299","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"}