On the subgroup structure of exceptional groups of Lie type

DOI10.1090/S0002-9947-98-02121-7zbMath0905.20031OpenAlexW1924518719WikidataQ115284731 ScholiaQ115284731MaRDI QIDQ4211107

Gary M. Seitz, Martin W. Liebeck

Publication date: 10 September 1998

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-98-02121-7

zbMATH Keywords

maximal subgroupsalmost simple subgroupsfinite exceptional groups of Lie typeembeddings of algebraic groupssubgroups of algebraic groups

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Maximal subgroups (20E28) Series and lattices of subgroups (20D30) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (37)

Finite singular orbit modules for algebraic groups ⋮ GROUPS WITH EXACTLY TWO SUBGROUPS OF GIVEN ORDER ⋮ Maximal connected 𝑘-subgroups of maximal rank in connected reductive algebraic 𝑘-groups ⋮ Twisted tensor product subgroups of finite classical groups ⋮ Growth in finite simple groups of Lie type ⋮ Split buildings of type \(\mathsf {F}_4\) in buildings of type \(\mathsf {E}_6\) ⋮ Maximal 𝑃𝑆𝐿₂ Subgroups of Exceptional Groups of Lie Type ⋮ Modules for algebraic groups with finitely many orbits on subspaces ⋮ On the involution fixity of exceptional groups of Lie type ⋮ Irredundant bases for finite groups of Lie type ⋮ Sublattices generated by root differences ⋮ The maximal subgroups of the exceptional groups \(F_4(q)\), \(E_6(q)\) and \(^2\!E_6(q)\) and related almost simple groups ⋮ Irreducible \(A_1\) subgroups of exceptional algebraic groups ⋮ On Medium-Rank Lie Primitive and Maximal Subgroups of Exceptional Groups of Lie Type ⋮ Complete reducibility and Steinberg endomorphisms. ⋮ Zero-one generation laws for finite simple groups ⋮ Large subgroups of simple groups. ⋮ Simple irreducible subgroups of exceptional algebraic groups. ⋮ -TYPE SUBGROUPS CONTAINING REGULAR UNIPOTENT ELEMENTS ⋮ On a conjecture of G. E. Wall. ⋮ On Non-Generic Finite Subgroups of Exceptional Algebraic Groups ⋮ A conjecture on product decompositions in simple groups. ⋮ Irreducible disconnected subgroups of exceptional algebraic groups. ⋮ Overgroups of subsystem subgroups in exceptional groups: levels. ⋮ Regular orbits of quasisimple linear groups. II ⋮ Calculations in exceptional groups, an update. ⋮ Normalizer of the Chevalley group of type ${\operatorname E}_7$ ⋮ The reductive subgroups of $F_4$ ⋮ The reductive subgroups of G 2 ⋮ Probabilistic and Asymptotic Aspects of Finite Simple Groups ⋮ Algorithms determining finite simple images of finitely presented groups ⋮ Subgroups of type \(A_1\) containing a fixed unipotent element in an algebraic group ⋮ The maximal subgroups of ⋮ Random generation of finite simple groups ⋮ On finite linear spaces with almost simple flag-transitive automorphism groups ⋮ A new maximal subgroup of 𝐸₈ in characteristic 3 ⋮ Variations on a theme of Steinberg.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Representations and maximal subgroups of finite groups of Lie type
• Just non hypercentral elements and the Bell-centre
• Extending morphisms from finite to algebraic groups
• Some representations of exceptional Lie algebras
• A construction of certain maximal subgroups of the algebraic groups \(E_ 6\) and \(F_ 4\)
• On finite groups of Lie type and odd characteristic
• Rational and generic cohomology
• Flag-transitive subgroups of Chevalley groups
• Subgroups generated by root elements in groups of Lie type
• Subgroups of type \(A_1\) containing semiregular unipotent elements.
• Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I
• Maximal subgroups of exceptional groups of Lie type, finite and algebraic
• Filtrations of cohomology modules for Chevalley groups
• The local structure of finite groups of characteristic 2 type
• On the Orders of Maximal Subgroups of the Finite Classical Groups
• Centralizers of Semisimple Elements in Finite Twisted Groups of Lie Type
• The maximal subgroups of classical algebraic groups
• Irreducible subgroups of exceptional algebraic groups
• WEIGHTS OF INFINITESIMALLY IRREDUCIBLE REPRESENTATIONS OF CHEVALLEY GROUPS OVER A FIELD OF PRIME CHARACTERISTIC
• The Projective Indecomposable Modules of SL(2, p ⁿ )
• Maximal subgroups of exceptional algebraic groups
• Extensions of Simple Modules for SL₃ (2 ⁿ ) and SU₃ (2 ⁿ )
• 𝐴₁ subgroups of exceptional algebraic groups
• Reductive subgroups of exceptional algebraic groups
• Simple Subgroups of Large Rank in Groups of Lie Type

This page was built for publication: On the subgroup structure of exceptional groups of Lie type