A new look at the decomposition of unipotents and the normal structure of Chevalley groups

DOI10.1090/spmj/1456zbMath1392.20041arXiv1512.02299OpenAlexW2963959856MaRDI QIDQ2970918

Alexei Stepanov

Publication date: 31 March 2017

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.02299

zbMATH Keywords

normal structureChevalley groupsgeneric elementparabolic subgroupuniversal localizationunipotent element

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Commutator calculus (20F12) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Linear algebraic groups over adèles and other rings and schemes (20G35) Congruence subgroup problems (19B37)

Related Items (6)

On the normalizer of a unipotent root subgroup in a Chevalley group ⋮ Sandwich classification for \(\mathrm{GL}_{n}(R)\), \(\mathrm{O}_{2n}(R)\) and \(\mathrm{U}_{2n}(R,\lambda)\) revisited ⋮ Toward the reverse decomposition of unipotents. II: The relative case ⋮ Sandwich classification for \(O_{2n+1}(R)\) and \(U_{2n+1}(R,\Delta)\) revisited ⋮ Towards the reverse decomposition of unipotents ⋮ The reverse decomposition of unipotents for bivectors

Cites Work

• Structure of Chevalley groups over rings via universal localization.
• Location of subgroups in the general linear group over a commutative ring
• Decomposition of transvections: A theme with variations
• Basic reductions in the description of normal subgroups.
• Schémas en groupes. I: Propriétés générales des schémas en groupes. Exposés I à VIIb. Séminaire de Géométrie Algébrique 1962/64, dirigé par Michel Demazure et Alexander Grothendieck. Revised reprint
• ON THE STABILIZATION OF THE GENERAL LINEAR GROUP OVER A RING
• Generators, Relations and Coverings of Chevalley Groups Over Commutative Rings
• On normal subgroups of Chevalley groups over commutative rings
• On normal subgroups of Chevalley groups over commutative rings
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