The 27-dimensional module for \(E_ 6\). IV

DOI10.1016/0021-8693(90)90164-JzbMath0698.20031MaRDI QIDQ912213

Michael Aschbacher

Publication date: 1990

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

geometryisometriesDynkin diagramclosed subgroupuniversal Chevalley group27-dimensional vector spaceBaer-Suzuki Theoremnonabelian simple groupsymmetric trilinear form

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) Simple groups (20E32) 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 (22)

Subgroups generated by root-elements of groups generated by \(k\)-root subgroups ⋮ Geometry of root elements in groups of type $\mathrm E_{6}$ ⋮ Receding polar regions of a spherical building and the center conjecture. ⋮ 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) ⋮ Overgroups of $\mathrm{EO}(n,R)$ ⋮ 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 ⋮ A description of Baer-Suzuki type of the solvable radical of a finite group. ⋮ Embeddings of the group \(L(2,13)\) in groups of Lie type \(E_ 6\) ⋮ On extensions of the Baer-Suzuki theorem ⋮ Subgroups of Lie type groups containing a unipotent radical. ⋮ A geometry of the generalized quadrangle (Ω,𝔏) of type O6−(2) and Lie algebras of type E6 with characteristic two ⋮ 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 ⋮ Unnamed Item ⋮ Abstract root subgroups and quadratic action. With an Appendix by A. E. Zalesskii ⋮ Width of groups of type $\mathrm E_{6}$ with respect to root elements. I

Cites Work

• Chevalley groups of type \(G_ 2\) as the group of a trilinear form
• Some subgroups of \(SI_ n(F_2)\)
• Some groups generated by transvections
• The 27-Dimensional Module for E₆ , II
• Involutions in Chevalley groups over fields of even order

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