A quick geometrical proof that \(G_ 2(K)\) is maximal in \(P\Omega _ 7(K)\)

DOI10.1007/BF00183027zbMath0645.51016MaRDI QIDQ1103193

Roger H. Dye

Publication date: 1988

Published in: Geometriae Dedicata (Search for Journal in Brave)

zbMATH Keywords

trialityquadricsimple groupChevally exceptional group

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Simple groups: alternating groups and groups of Lie type (20D06) Orthogonal and unitary groups in metric geometry (51F25)

Related Items

The simple exceptional group \(G_2(q), q\) even, and two-character sets ⋮ Some two-character sets ⋮ The Action of the Group, q Even, and Related Combinatorial Structures ⋮ On subgroups of the group \(GL_7\) over a field that contain a Chevalley group of type \(G_2\) over a subfield. ⋮ On the geometry of the exceptional group \(G_2(q)\), \(q\) even ⋮ Interrelations of symplectic and orthogonal groups in characteristic two

Cites Work

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• On the maximal subgroups of the finite classical groups
• On the Orders of Maximal Subgroups of the Finite Classical Groups
• Subgroups of Classical Groups Generated by Long Root Elements
• Some Geometry of Triality with Applications to Involutions of Certain Orthogonal Groups