AN A3-PROOF OF STRUCTURE THEOREMS FOR CHEVALLEY GROUPS OF TYPES E6 AND E7
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Publication:5386967
DOI10.1142/S0218196707003998zbMath1172.20034MaRDI QIDQ5386967
Publication date: 14 May 2008
Published in: International Journal of Algebra and Computation (Search for Journal in Brave)
parabolic subgroupselementary subgroupspresentationsnormal subgroupsChevalley groupsSteinberg groupsminimal modulesdecomposition of unipotentsstandard descriptionsroot elementsproof from the Bookcentrality of \(K_2\)orbit of highest weight vector
Related Items
Geometry of root elements in groups of type $\mathrm E_{6}$ ⋮ Decomposition of transvections for automorphisms. ⋮ Bak's work on theK-theory of rings ⋮ Standardness and standard automorphisms of Chevalley groups. I: The case of rank at least two. ⋮ Calculations in exceptional groups over rings. ⋮ Chevalley groups of type \(E_7\) in the 56-dimensional representation. ⋮ Width of groups of type \(\mathrm E_6\) with respect to root elements. II. ⋮ Decomposition of unipotents for \(\mathrm{E}_6\) and \(\mathrm{E}_7\): 25 years after ⋮ Relative subgroups in Chevalley groups ⋮ More variations on the decomposition of transvections. ⋮ Automorphisms of Chevalley groups of type \(B_l\) over local rings with \(1/2\). ⋮ Automorphisms of Chevalley groups of types \(A_l\), \(D_l\), \(E_l\) over local rings without \(1/2\). ⋮ Can one see the signs of structure constants? ⋮ Chevalley groups of type E7 in the 56-dimensional representation ⋮ Yet another variation on the theme of decomposition of transvections. ⋮ Normalizer of the Chevalley group of type ${\mathrm E}_6$ ⋮ $\mathrm A_2$-proof of structure theorems for Chevalley groups of type $\mathrm F_4$ ⋮ Numerology of square equations ⋮ Overgroups of $\text {\rm F}_4$ in $\text {\rm E}_6$ over commutative rings ⋮ Calculations in exceptional groups, an update. ⋮ Normalizer of the Chevalley group of type ${\operatorname E}_7$ ⋮ Width of groups of type $\mathrm E_{6}$ with respect to root elements. I ⋮ ${\mathrm A}_3$-proof of structure theorems for Chevalley groups of types ${\mathrm E}_6$ and ${\mathrm E}_7$ II. Main lemma ⋮ Basic reductions in the description of normal subgroups.
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