Subgroups isomorphic to \(G_2(L)\) in orthogonal groups

DOI10.1006/jabr.1997.7375zbMath0914.20042OpenAlexW2025131617MaRDI QIDQ1271010

A. I. Steinbach

Publication date: 20 June 1999

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

Full work available at URL: https://doi.org/10.1006/jabr.1997.7375

zbMATH Keywords

orthogonal groupssemilinear mappingslong root elementsembeddings of groupsSiegel transvections

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Subgroup theorems; subgroup growth (20E07) Orthogonal and unitary groups in metric geometry (51F25)

Related Items (6)

Geometry of root elements in groups of type $\mathrm E_{6}$ ⋮ On subloops of the loop of invertible elements of the split Cayley–Dickson algebra over a field that contain a subloop of transvections ⋮ On subgroups of the group \(GL_7\) over a field that contain a Chevalley group of type \(G_2\) over a subfield. ⋮ Geometry of 1-tori in $\mathrm {GL}_n$ ⋮ Weak embeddings of generalized hexagons and groups of type G2 ⋮ Groups of Lie type generated by long root elements in \(F_4(K)\).

Cites Work

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• Homomorphismes abstraits de groupes algébriques simples
• Chevalley groups of type \(G_ 2\) as the group of a trilinear form
• Abstract root subgroups and quadratic action. With an Appendix by A. E. Zalesskii
• Subgroups of classical groups generated by transvections or Siegel transvections. I: Embeddings in linear groups
• Quadratic modules for CHEVALLEY groups over fields of odd characteristics
• Subgroups of Classical Groups Generated by Long Root Elements

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