Subgroups of type \(A_1\) containing a fixed unipotent element in an algebraic group

DOI10.1006/jabr.2000.8353zbMath0981.20035OpenAlexW2062341042MaRDI QIDQ1584605

Jan Saxl, Richard Proud, Donna M. Testerman

Publication date: 5 December 2001

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

Full work available at URL: https://doi.org/10.1006/jabr.2000.8353

zbMATH Keywords

finite groups of Lie typegraph morphismsunipotent elementssimple algebraic groupsFrobenius morphismssubgroups of type \(A_1\)

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Subgroup theorems; subgroup growth (20E07) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (8)

Unnamed Item ⋮ Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with a single non-trivial Jordan block ⋮ Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VI. Suzuki and Ree groups ⋮ -TYPE SUBGROUPS CONTAINING REGULAR UNIPOTENT ELEMENTS ⋮ Unipotent elements forcing irreducibility in linear algebraic groups ⋮ Irreducibility in algebraic groups and regular unipotent elements ⋮ Unipotent Overgroups in Simple Algebraic Groups ⋮ Geometry of word equations in simple algebraic groups over special fields

Cites Work

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• The maximal subgroups of \({}^ 2F_ 4(q^ 2)\)
• Some Coset Actions in G ₂ (q )
• Automorphisms of Finite Linear Groups
• A Family of Simple Groups Associated with the Simple Lie Algebra of Type (G 2 )
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• Centralizers of Semisimple Elements in Finite Groups of Lie Type
• On the subgroup structure of exceptional groups of Lie type
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