The 27-Dimensional Module for E 6 , III

DOI10.2307/2001591zbMath0698.20030OpenAlexW4251407342MaRDI QIDQ3475472

Michael Aschbacher

Publication date: 1990

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2001591

zbMATH Keywords

actionisometriesstabilizeruniversal Chevalley groupsymmetric trilinear formclosed solvable subgroup

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Linear algebraic groups over finite fields (20G40) Subgroup theorems; subgroup growth (20E07) Maximal subgroups (20E28) Quadratic forms over general fields (11E04) Geometric group theory (20F65) Representations of groups as automorphism groups of algebraic systems (20F29) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (17)

Geometry of root elements in groups of type $\mathrm E_{6}$ ⋮ Classification of some 3-subgroups of the finite groups of Lie type \(E_{6}\) ⋮ The maximal subgroups of the exceptional groups \(F_4(q)\), \(E_6(q)\) and \(^2\!E_6(q)\) and related almost simple groups ⋮ On Medium-Rank Lie Primitive and Maximal Subgroups of Exceptional Groups of Lie Type ⋮ An analog of albert’s Jordan 27-dimensional algebra over a field K of characteristic two and its automorphism group F ₄ (K) ⋮ On root-involutions and root-subgroups of E6(K) for fields K of characteristic two ⋮ On Cameron's question about primitive permutation groups with stabilizer of two points that is normal in the stabilizer of one of them. ⋮ Width of groups of type \(\mathrm E_6\) with respect to root elements. II. ⋮ Unnamed Item ⋮ Orbits of vectors in some representations. I ⋮ On Non-Generic Finite Subgroups of Exceptional Algebraic Groups ⋮ Embeddings of the group \(L(2,13)\) in groups of Lie type \(E_ 6\) ⋮ Chevalley groups of type E7 in the 56-dimensional representation ⋮ A geometry of the generalized quadrangle (Ω,𝔏) of type O6−(2) and Lie algebras of type E6 with characteristic two ⋮ Unnamed Item ⋮ Width of groups of type $\mathrm E_{6}$ with respect to root elements. I ⋮ Imprimitive irreducible modules for finite quasisimple groups

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