Construction of Some Irreducible Subgroups of E8 and E6

DOI10.1112/S1461157000001431zbMath1223.20042OpenAlexW2015608294MaRDI QIDQ3091951

Alexander J. E. Ryba

Publication date: 15 September 2011

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s1461157000001431

zbMATH Keywords

finite subgroupsembeddingsgroups of Lie typeLie primitive subgroupsminimal modulessimple algebraic groups of exceptional typecomputer constructions

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Subgroup theorems; subgroup growth (20E07) Maximal subgroups (20E28) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (3)

Recognition of absolutely irreducible matrix groups that are tensor decomposable or induced ⋮ The maximal subgroups of the exceptional groups \(F_4(q)\), \(E_6(q)\) and \(^2\!E_6(q)\) and related almost simple groups ⋮ Calculations in exceptional groups over rings.

Uses Software

• ATLAS Group Representations

Cites Work

• Automorphisms of classical Lie algebras
• Computer construction of split Cartan subalgebras
• Identification of matrix generators of a Chevalley group.
• Embeddings of \(\text{SL}(2,27)\) in complex exceptional algebraic groups.
• Short proofs of embeddings into exceptional groups of Lie type
• Characters of Elements of Finite Order in Lie Groups
• The modular characters of the tits simple group and its automorphism group
• Finite Subgroups of F ₄ (C) and E ₆ (C)
• Subgroups of exceptional algebraic groups which are irreducible on an adjoint or minimal module
• Matrix generators for the Harada–Norton group

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