{"paper":{"title":"Generation of relative commutator subgroups in Chevalley groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Nikolai Vavilov, Roozbeh Hazrat, Zuhong Zhang","submitted_at":"2012-12-21T13:49:28Z","abstract_excerpt":"Let $\\Phi$ be a reduced irreducible root system of rank $\\ge 2$, let $R$ be a commutative ring and let $I,J$ be two ideals of $R$. In the present paper we describe generators of the commutator groups of relative elementary subgroups $\\big[E(\\Phi,R,I),E(\\Phi,R,J)\\big]$ both as normal subgroups of the elementary Chevalley group $E(\\Phi,R)$, and as groups. Namely, let $x_{\\a}(\\xi)$, $\\a\\in\\Phi$, $\\xi\\in R$, be an elementary generator of $E(\\Phi,R)$. As a normal subgroup of the absolute elementary group $E(\\Phi,R)$, the relative elementary subgroup is generated by $x_{\\a}(\\xi)$, $\\a\\in\\Phi$, $\\xi\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5432","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":""},"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"}