Embeddings of \(\text{PGL}_2(31)\) and \(\text{SL}_2(32)\) in \(E_8(\mathbb{C})\). With appendices by Michael Larsen and J. -P. Serre

DOI10.1215/S0012-7094-98-09409-1zbMath0980.20035MaRDI QIDQ1974835

Robert L. jun. Griess, Alexander J. E. Ryba

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

conjugacy classesalgebraic groupsfinite simple groupsembeddingsliftingsfinite simple subgroupsquasisimple algebraic groups

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Linear algebraic groups over finite fields (20G40) Simple groups: sporadic groups (20D08) Subgroup theorems; subgroup growth (20E07) Simple groups (20E32) Representation theory for linear algebraic groups (20G05) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Finite simple groups and their classification (20D05) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (4)

On conjugacy classes of maximal subgroups of finite simple groups, and a related zeta function. ⋮ The maximal subgroups of the exceptional groups \(F_4(q)\), \(E_6(q)\) and \(^2\!E_6(q)\) and related almost simple groups ⋮ Embeddings of \(\text{PSL}(2,41)\) and \(\text{PSL}(2,49)\) in \(E_8(\mathbb{C})\) ⋮ Equivalences between fusion systems of finite groups of Lie type

Cites Work

• Elementary abelian p-subgroups of algebraic groups
• Unrefined minimal \(K\)-types for \(p\)-adic groups
• Examples for embeddings of groups \(\text{PSL}_ 2(F_ p)\) into simple Lie groups
• Maximality of Galois actions for compatible systems
• Galois-Kohomologie halb einfacher algebraischer Gruppen über \(p\)-adischen Körpern. I, II
• Algebraic approximation of structures over complete local rings
• Remarks on the cohomology of groups
• First cohomology groups of some linear groups over fields of characteristic two
• On some Bruhat decomposition and the structure of the Hecke rings of \(p\)-adic Chevalley groups
• Subfields and automorphism groups of \(p\)-adic fields
• The groupL(2 61) embeds in t h e Lie group of typeE₈
• On the Structure and Ideal Theory of Complete Local Rings
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