Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Factorizations of simple algebraic groups

Authors: Martin W. Liebeck, Jan Saxl and Gary M. Seitz
Journal: Trans. Amer. Math. Soc. 348 (1996), 799-822
MSC (1991): Primary 20G15
MathSciNet review: 1316858
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We determine all factorizations of simple algebraic groups as the product of two maximal closed connected subgroups. Additional results are established which drop the maximality assumption, and applications are given to the study of subgroups of classical groups transitive on subspaces of a given dimension.

References [Enhancements On Off] (What's this?)

  • Bo A. Borel, Linear algebraic groups, 2nd ed., Springer-Verlag, New York, 1991. MR 92d:20001
  • Bou N. Bourbaki, Groupes et algèbres de Lie, Chapter 4, Hermann, Paris, 1968. MR 39:1590
  • Ca R. W. Carter, Conjugacy classes in the Weyl group, Compositio Math. 25 (1972), 1--59. MR 47:6884
  • CLSS A. M. Cohen, M.W. Liebeck, J. Saxl, and G. M. Seitz, The local maximal subgroups of exceptional groups of Lie type, finite and algebraic, Proc. London Math. Soc. 64 (1992), 21--48. MR 92m:20012
  • Ha W. J. Haboush, Homogeneous vector bundles and reductive subgroups of reductive algebraic groups, Amer. J. Math. 100 (1978), 1123--1137. MR 80f:14007
  • Hu J. E. Humphreys, Linear algebraic groups, Graduate Texts in Math., No. 21, Springer, 1975. MR 53:633
  • Ka I. L. Kantor, Cross-ratio of four points and other invariants on homogeneous spaces with parabolic isotropy groups, Trudy Sem. Vektor. Tenzor. Anal. 17 (1974), 250--313. MR 50:7176
  • KST P. B. Kleidman, G.M. Seitz and D.M. Testerman, preprint.
  • Li M. W. Liebeck, The affine permutation groups of rank three, Proc. London Math. Soc. 54 (1987), 477--516. MR 88m:20004
  • LPS M. W. Liebeck, C.E. Praeger, and J. Saxl, The maximal factorizations of the finite simple groups and their automorphism groups, Mem. Amer. Math. Soc., Vol. 86, No. 432 (1990), 1--151. MR 90k:20048
  • LS1 M. W. Liebeck and G.M. Seitz, Subgroups containing root elements in groups of Lie type, Annals of Math. (2) 139 (1994), 293--361. MR 95d:20078
  • LS2 ------, Reductive subgroups of exceptional algebraic groups, Mem. Amer. Math. Soc. (to appear).
  • On A. L. Onishchik, Parabolic factorizations of semisimple algebraic groups, Math. Nachr. 104 (1981), 315--329. MR 83h:20041
  • Ri R. W. Richardson, Affine coset spaces of reductive algebraic groups, Bull. London Math. Soc. 9 (1977), 38--41. MR 55:10473
  • Se1 G. M. Seitz, The maximal subgroups of classical algebraic groups, Mem. Amer. Math. Soc., Vol. 67, No. 365 (1987), 1--286. MR 88g:20092
  • Se2 ------, The maximal subgroups of exceptional algebraic groups, Mem. Amer. Math. Soc., Vol. 90, No. 441 (1991), 1--197. MR 91g:20038
  • SS T. A. Springer and R. Steinberg, Conjugacy classes, Seminar on Algebraic Groups and Related Topics (A. Borel et al., eds.), Lecture Notes in Math., vol. 131, Springer, Berlin, 1970, pp. 168--266. MR 42:3091
  • St1 R. Steinberg, Lectures on Chevalley groups, Yale University Lecture Notes, 1968.
  • St2 ------, Conjugacy classes in algebraic groups, Lecture Notes in Math., vol. 366, Springer, Berlin, 1974. MR 50:4766

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 20G15

Retrieve articles in all journals with MSC (1991): 20G15

Additional Information

Martin W. Liebeck
Affiliation: Department of Mathematics, Imperial College, London SW7 2BZ, England

Jan Saxl
Affiliation: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, England

Gary M. Seitz
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403

Received by editor(s): May 3, 1994
Received by editor(s) in revised form: January 30, 1995
Article copyright: © Copyright 1996 American Mathematical Society