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Subgroups of compact Lie groups containing a maximal torus are closed

Author: Dragomir Ž. Djoković
Journal: Proc. Amer. Math. Soc. 83 (1981), 431-432
MSC: Primary 22E15; Secondary 20G20
MathSciNet review: 624947
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Abstract: We prove the claim made in the title. As a corollary, we obtain that a compact Lie group $ G$ has only finitely many subgroups containing a fixed maximal torus. The special case $ G = U(n)$ was dealt with in a recent paper of Borevich and Krupeckiĭ.

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

  • [1] A. Borel and J. de Siebenthal, Les sous-groupes fermés de rang maximum des groupes de Lie clos, Comment. Math. Helv. 23 (1949), 200-221. MR 0032659 (11:326d)
  • [2] Z. I. Borevich and S. L. Krupeckiĭ, Subgroups of the unitary group containing the group of diagonal matrices, Zap. Naučn. Sem. Leningrad Otdel. Mat. Inst. Steklov (LOMI) 86 (1979), 19-29. MR 535476 (81e:20051)
  • [3] M. Goto, On an arcwise connected subgroup of a Lie group, Proc. Amer. Math. Soc. 20 (1969), 157-162. MR 0233923 (38:2244)
  • [4] J. Wolf, Spaces of constant curvature, 2nd ed., Dept. of Math., Univ. of Calif., Berkeley, 1972. MR 0343213 (49:7957)

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