Ukrainian Mathematical Journal

, Volume 42, Issue 2, pp 145–148 | Cite as

Compact elements and Cartan subgroups of connected Lie groups

  • M. I. Kabenyuk


It is established that the number of compact Cartan subgroups of a connected Lie group is determined by the topological size of the set of its compact elements. This fact clarifies the structure of those connected Lie groups in which the set indicated is everywhere dense.


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Literature cited

  1. 1.
    V. P. Platonov, “Periodic and compact subgroups of topological groups,” Sib. Mat. Zh.,39, No. 4, 854–877 (1966).Google Scholar
  2. 2.
    D. Z. Djokovic, “The union of compact subgroups of a connected locally compact group,” Math. Z.,185, No. 2, 99–105 (1978).Google Scholar
  3. 3.
    M. I. Kabenyuk, “Connected groups with dense sets of compact elements,” Ukr. Mat. Zh.,33, No. 2, 179–183 (1981).Google Scholar
  4. 4.
    C. Chevalley, Theory of Lie Groups. III [Russian translation], Izdat. Inostr. Lit., Moscow (1958).Google Scholar
  5. 5.
    M. I. Kabenyuk, “Compact elements and Cartan subgroups of connected Lie groups,” in: Tenth National Symposium on Group Theory: Abstracts of Reports [in Russian], Inst. Mat. AN BSSR, Minsk (1986).Google Scholar
  6. 6.
    N. Bourbaki, Lie Groups and Algebras, Chapter VIII [Russian translation], Mir, Moscow (1978).Google Scholar
  7. 7.
    A. I. Malcev, “On the theory of the Lie groups in the large,” Mat. Sb.,16, No. 2, 163–189 (1945).Google Scholar
  8. 8.
    G. Warner, Harmonic Analysis on Semi-Simple Lie Groups. I, Springer, Berlin (1972).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • M. I. Kabenyuk
    • 1
  1. 1.Kemerovo UniversityUSSR

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