Journal of Mathematical Sciences

, Volume 116, Issue 1, pp 3035–3041

The Arrangement of Long and Short Root Subgroups in a Chevalley Group of Type G2

  • V. V. Nesterov


The subgroups generated by a long and a short root subgroup in a Chevalley group of type G2 are described, and the orbits of the group acting on such pairs by simultaneous conjugation are classified. Bibliography: 18 titles.


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  1. 1.
    N. A. Vavilov, “Geometry of long root subgroups in Chevalley groups," Vestn. Leningr. Univ., Mat., 21, No. 1, 5-10 (1988).Google Scholar
  2. 2.
    N. A. Vavilov, “Mutual arrangement of long and short root subgroups in a Chevalley group," Vestn. Leningr. Univ., Mat., 22, No. 1, 1-7 (1989).Google Scholar
  3. 3.
    N. A. Vavilov, “Subgroups of Chevalley groups containing a maximal torus," Trudy Leningr. Mat. Soc., 1, 64-109 (1990).Google Scholar
  4. 4.
    A. S. Kondrat'ev, “Subgroups of finite Chevalley groups," Usp. Mat. Nauk, 41, No. 1, 57-96 (1986).Google Scholar
  5. 5.
    V. V. Nesterov, “Pairs of short root subgroups in a Chevalley group," Dokl. Ross. Akad. Nauk, 357, 302-305 (1997).Google Scholar
  6. 6.
    R. Steinberg, Lectures on Chevalley Groups, Yale University (1967).Google Scholar
  7. 7.
    M. Aschbacher and G. M. Seitz, “Involutions in Chevalley groups over fields of even order," Nagoya Math. J., 63, 1-91 (1976).Google Scholar
  8. 8.
    R. W. Carter, Simple Groups of Lie Type, Wiley, London (1972).Google Scholar
  9. 9.
    B. N. Cooperstein, “The geometry of root subgroups in exceptional groups," Geometria Dedicata, 8, No.3, 317-381 (1979).Google Scholar
  10. 10.
    B. N. Cooperstein, “Geometry of long root subgroups in groups of Lie type," Proc. Symp. Pure Math., 37, 243-248 (1980).Google Scholar
  11. 11.
    B. N. Cooperstein, “Maximal subgroups of G2(2 n )," J. Algebra, 37, No. 1, 23-36 (1981).Google Scholar
  12. 12.
    J. Hurrelbrink and U. Rehmann, “Eine endliche Präsentation der Gruppe G2( Z )," Math. Z., 141, 243-251 (1975).Google Scholar
  13. 13.
    W. M. Kantor, “Subgroups of classical groups generated by long root elements," Trans. Math. Soc., 248, No. 2, 347-379 (1979).Google Scholar
  14. 14.
    W. M. Kantor, “Generation of linear groups," in: The Geometrical Vein: Coxeter Festschift, Springer-Verlag, Berlin (1981), pp. 497-509.Google Scholar
  15. 15.
    Li Shang Zhi, “Maximal subgroups containing short root subgroups in PSp(2n; F )," Acta Math. Sinica, New Ser., 3, No. 1, 82-91 (1987).Google Scholar
  16. 16.
    B. S. Stark, “Some subgroups of (V ) generated by groups of root type," J. Algebra, 17, No. [sn1], 33-41 (1974).Google Scholar
  17. 17.
    B. S. Stark, “Irreducible subgroups of orthogonal groups generated by groups of root type 1," Pacific J. Math., 53, No. 2, 611-625 (1974).Google Scholar
  18. 18.
    F. G. Timmesfeld, “Groups generated by k-root subgroups,” Invent. Math., 106, 575-666 (1991).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • V. V. Nesterov
    • 1
  1. 1.The Baltic State Technical UniversitySt.Petersburg

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