Abstract Root Subgroups and Quadratic Action

✍ Scribed by F.G. Timmesfeld

• Book ID: 102966957
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 893 KB
• Volume: 142
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1998.1779

✦ Synopsis

Basic topics. 2. Rank 1 groups. 3. Abstract root subgroups. 4. Triangle groups. II. The classification of groups generated by abstract transvection groups. 5. The radical R(G). 6. Proof of Theorem 3. 7. Proof of Theorem 4. III. The nondegenerate case I: Weak imprimitivity. 8. 7-subgroups. 9. The action of G on 7. 10. Weak TI-subsets. 11. Classification of groups which are not primitive on 7. 12. Moufang hexagons. IV. The nondegenerate case II: G primitive on 7. 13. More general properties. 14. The orthogonal and symplectic groups. 15. The action on the radical R(G). 16. Metasymplectic spaces. 17. E 6 (k), E 7 (k) and E 8 (k). 18. Proof of Theorems 5 and 6. V. Quadratic pairs. 19. Some matrix groups. 20. The SL 2 -Lemma. 21. Opposites. 22. Unipotent subgroups. 23. Proof of Theorem 1 and 2. Appendix References

1. M is an irreducible kG-module, 2. G=( Q); where Q is the set of quadratic elements _ of G satisfying k b _ G.