$\mathrm A_2$-proof of structure theorems for Chevalley groups of type $\mathrm F_4$

DOI10.1090/S1061-0022-09-01060-7zbMath1206.20055OpenAlexW1553966419MaRDI QIDQ3079262

Sergey I. Nikolenko, Nikolai A. Vavilov

Publication date: 2 March 2011

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

Full work available at URL: https://doi.org/10.1090/s1061-0022-09-01060-7

zbMATH Keywords

parabolic subgroupselementary subgroupsnormal subgroupsChevalley groupsdecompositions of unipotentsroot elementsstandard descriptionminimal moduleorbits of weight vectorsproof from the Book

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Chains and lattices of subgroups, subnormal subgroups (20E15) Linear algebraic groups over adèles and other rings and schemes (20G35) Exceptional groups (20G41)

Related Items

Relative centralizers of relative subgroups, Standardness and standard automorphisms of Chevalley groups. I: The case of rank at least two., Sandwich classification for \(\mathrm{GL}_{n}(R)\), \(\mathrm{O}_{2n}(R)\) and \(\mathrm{U}_{2n}(R,\lambda)\) revisited, Relative commutator calculus in Chevalley groups., Decomposition of unipotents for \(\mathrm{E}_6\) and \(\mathrm{E}_7\): 25 years after, Sandwich classification for \(O_{2n+1}(R)\) and \(U_{2n+1}(R,\Delta)\) revisited, Towards the reverse decomposition of unipotents, Localization-completion strikes again: relative \(K_1\) is nilpotent by Abelian, Normalizer of the Chevalley group of type ${\mathrm E}_6$, Calculations in exceptional groups, an update., Subgroups of symplectic groups that contain a subsystem subgroup.

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