Maximal Textrm {PSL}_2 Subgroups of Exceptional Groups of Lie Type

• Autore: Craven David A
• Pubblicazione: Providence : , : American Mathematical Society, , 2022; ©2022
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (168 pages)
• Disciplina: 512/.482; 512.482
• Soggetto topico: Lie groups; Maximal subgroups; Exceptional Lie algebras; Group theory and generalizations -- Abstract finite groups -- Simple groups: alternating groups and groups of Lie type; Group theory and generalizations -- Linear algebraic groups and related topics -- Exceptional groups
• Classificazione: 20D0620G41
• Nota di contenuto: Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Notation and Preliminaries -- Chapter 3. Maximal Subgroups -- Chapter 4. Maximal Subgroups and Subspace Stabilizers -- Chapter 5. Blueprint Theorems for Semisimple Elements -- 5.1. Preliminary Results -- 5.2. Determination of the Bounds for the Minimal Module -- 5.3. Consequences for Maximal Subgroups -- Chapter 6. Unipotent and Semisimple Elements -- 6.1. Actions of Unipotent Elements -- 6.2. Blueprints and Element Orders -- 6.3. Blueprints inside Subgroups of Type ₁ -- 6.4. Traces of Modules for \PGL₂ -- 6.5. The Graph Automorphism of ₄ -- 6.6. Rank-1 Subalgebras of the Lie Algebra -- Chapter 7. Modules for \SL₂ -- 7.1. Modules for \SL₂(2^{ }) -- 7.2. Modules for \SL₂(3^{ }) -- 7.3. Modules for \SL₂( ) -- 7.4. Modules for \SL₂( ^{ }) for ≥5 and > -- 1 -- Chapter 8. Some \PSL₂s inside ₆ in Characteristic 3 -- Chapter 9. Proof of the Theorems: Strategy -- Chapter 10. The Proof for ₄ -- 10.1. Characteristic 2 -- 10.2. Characteristic 3 -- 10.3. Characteristic At Least 5 -- Chapter 11. The Proof for ₆ -- 11.1. Characteristic 2 -- 11.2. Characteristic 3 -- 11.3. Characteristic At Least 5 -- Chapter 12. The Proof for ₇ in Characteristic 2 -- Chapter 13. The Proof for ₇ in Odd Characteristic: \PSL₂ Embedding -- 13.1. Characteristic 3 -- 13.2. Characteristic At Least 5 -- Chapter 14. The Proof for ₇ in Odd Characteristic: \SL₂ Embedding -- 14.1. Characteristic 3 -- 14.2. Characteristic At Least 5 -- Appendix A. Actions of Maximal Positive-Dimensional Subgroups on Minimal and Adjoint Modules -- Appendix B. Traces of Small-Order Semisimple Elements -- Bibliography -- Back Cover.
• Sommario/riassunto: "We study embeddings of PSL2(pa) into exceptional groups G(pb) for G = F4, E6, 2E6, E7, and p a prime with a, b positive integers. With a few possible exceptions, we prove that any almost simple group with socle PSL2(pa), that is maximal inside an almost simple exceptional group of Lie type F44, E6, 2E6 and E7, is the fixed points under the Frobenius map of a corresponding maximal closed subgroup of type A1 inside the algebraic group. Together with a recent result of Burness and Testerman for p the Coxeter number plus one, this proves that all maximal subgroups with socle PSL2(pa) inside these finite almost simple groups are known, with three possible exceptions (pa = 7, 8, 25 for E7). In the three remaining cases we provide considerable information about a potential maximal subgroup"--
• Titolo autorizzato: Maximal Textrm {PSL}_2 Subgroups of Exceptional Groups of Lie Type
• ISBN: 9781470470210; 9781470451196
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910957558303321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society