Abstract root subgroups and quadratic action *

Advances in Mathematics

Volumn 142, Issue 1, 1999, Pages 1-150

  Timmesfeld, F G ^a  

^a JUSTUS LIEBIG UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033095958     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1998.1779     Document Type: Article

References (42)

1. M. Aschbacher, A characterization of chevalley-groups over fields of odd characteristic, Ann. of Math. 106 (1977), 353-468.
2. 6 IV, J. Algebra 131 (1990), 23-39.
3. 2 over an Infinite Field K." [Manuscript is kept in All Union Institutes of Scientific and Technical Information (VINITI), Moscow, No. 7369-84 Dep., and is copied by requests of readers.]
4. F. Buekenhout and E. F. Shult, On the foundations of polar geometry, Geom. Dedicata 3 (1974), 155-170.
5. P. Cameron and J. I. Hall, Some groups generated by transvection subgroups, J. Algebra 140 (1991), 184-209.
6. R. W. Carter, "Simple Groups of Lie-type," Wiley, New York, 1972.
7. A. M. Cohen, Point-line-spaces related to buildings, in "Handbook of Incidence Geometry, Buildings and Foundations" (F. Buekenhout, Ed.), Chap. 12, pp. 647-737, North-Holland, Amsterdam, 1995.
8. A. M. Cohen, An axiom system for metasymplectic spaces, Geom. Dedicata 12 (1982), 417-433.
9. A. M. Cohen and B. N. Cooperstein, A characterization of some geometries of lie type, Geom. Dedicata 15 (1983), 73-105.
10. B. N. Cooperstein, The geometry of root subgroups in exceptional groups I, Geom. Dedicata 8 (1979), 317-381.
11. B. N. Cooperstein, The geometry of root subgroups in exceptional groups II, Geom. Dedicata 15 (1983), 1-45.
12. H. Cuypers, The Geometry of K-transvection Groups, preprint.
13. 2(k) by Its Quadratic Action on the Natural Module, preprint.
14. H. Cuypers and J. H. Hall, The classification of 3-transposition groups with trivial center, in "Groups, Combinatorics and Geometry," Lecture Notes in Mathematics, Vol. 165, pp. 121-138, Springer-Verlag, Berlin/New York, 1992.
15. H. Cuypers, P. Johnson, and A. Pasini, On the embeddability of polar spaces, Geom. Dedicata 44 (1992), 349-358.
16. J. Dieudonné, "La Géométrie des Groupes Classiques" (Ergebnisse der Mathematik), Springer-Verlag, Berlin/New York, 1997.
17. J. R. Faulkner, Groups with steinberg relations and coordinatization of polygonal geometries, Mem. Amer. Math. Soc. 185 (1977).
18. C. Ho, On the quadratic pairs, J. Algebra 43 (1976), 338-358.
19. B. Huppert, "Endliche Gruppen I," Springer-Verlag, Berlin, 1967.
20. P. Johnson, Polar spaces of arbitrary rank, Geom. Dedicata 35 (1990), 229-250.
21. W. M. Kantor, Subgroups of classical groups generated by long root elements, Trans. Amer. Math. Soc. 248 (1979), 347-379.
22. M. W. Liebeck and G. M. Seitz, Subgroups generated by root elements in groups of lie type, Ann. of Math. 139 (1994), 293-361.
23. U. Meierfrankenfeld, A Characterization of the Natural Module of Some Classical Groups, preprint.
24. O. T. O'Meara and A. J. Hahn, "The classical groups and k-theory," Grundlehren der Math. Wiss., Vol. 291, Springer-Verlag, Berlin/New York.
25. G. Pickert, "Projektive Ebenen," Springer-Verlag, Berlin, 1955.
26. A. A. Premet and I. D. Suprunenko, Quadratic modules for chevalley groups over fields of odd characteristic, Math. Nachr. 110 (1983), 65-96.
27. M. Ronan, A geometric characterization of moufang hexagons, Invent. Math. 57 (1980), 227-262.
28. A. Steinbach, "Untergruppen von Klassischen Gruppen, die von Transvektionen oder Siegel-transvektionen Erzeugt Werden," Dissertation Giessen, 1995.
29. A. Steinbach, Subgroups of classical groups generated by transvections on Siegel transvections I, II, Geom. Dedicata 68 (1997), 281-322, 323-357.
30. A. Steinbach, Generalized quadrangles arising from groups generated by abstract transvection groups, in "Groups and Geometrics. Proceedings of the Conference, Siena, Italy, September 1-7, 1996" (L. Di Martino et al., Eds.), Trends in Mathematics, Birkhäuser, pp. 189-199, 1998.
31. J. Thompson, Quadratic pairs, in "Proc. of the International Congress of Mathematicians," Nice, 1970.
32. J. Thompson, Quadratic Pairs, unpublished.
33. F. G. Timmesfeld, Groups generated by k-transvections, Invent. Math. 100 (1990), 167-206.
34. F. G. Timmesfeld, Groups generated by k-root subgroups, Invent. Math. 106 (1991), 575-666.
35. F. G. Timmesfeld, Groups generated by k-root subgroups, a survey, in "Groups, Combinatorics and Geometry," Lecture Notes in Mathematics, Vol. 165, pp. 183-204, Springer-Verlag, Berlin/New York, 1992.
36. F. G. Timmesfeld, On the identification of natural modules for linear and symplectic groups over arbitrary fields, Geom. Dedicata 35 (1990), 127-142.
37. F. G. Timmesfeld, Subgroups generated by root elements of groups generated by k-root subgroups, Geom. Dedicata 49 (1994), 293-321.
38. 2(K), K a Cayley division algebra, Forum Math. 6 (1994), 209-231.
39. J. Tits, "Buildings of spherical type and finite bn-pairs," Lecture Notes in Mathematics, Vol. 386, Springer-Verlag, Berlin/New York, 1974.
40. J. Tits, Classification of algebraic semisimple groups, in "Proc. Symp. Pure Math IX," pp. 33-62, 1966.
41. J. Tits, Classification of buildings of spherical type and moufang polygons: A survey, Atti Conv. Lincei No. 17, in "Theorie Combinatorie," pp. 230-246, Acad. Nat. Lincei, Rome, 1976.
42. J. Tits, Moufang polygons, I. Root data, Bull. Belg. Math. Soc. 3 (1994), 455-468.