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Compact subgroups of Lie groups and locally compact groups


Authors: Karl H. Hofmann and Christian Terp
Journal: Proc. Amer. Math. Soc. 120 (1994), 623-634
MSC: Primary 22D05; Secondary 22E15
DOI: https://doi.org/10.1090/S0002-9939-1994-1166357-9
MathSciNet review: 1166357
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Abstract: We show that the set of compact subgroups in a connected Lie group is inductive. In fact, a locally compact group $ G$ has the inductivity property for compact subgroups if and only if the factor group $ G/{G_0}$ modulo the identity component has it.


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  • [1] R. W. Bagley, T. S. Wu, and J. S. Yang, Inverse limits and dense immersions of locally compact groups, Bull. Inst. Math. Acad. Sinica 19 (1991), 97-124. MR 1144126 (92j:22009)
  • [2] N. Bourbaki, Groupes et algèbres de Lie, Chapitres 1-9, Hermann (1-8), Masson (9), Paris, 1964-1982. MR 682756 (84i:22001)
  • [3] -, Intégration, Chapters 7 et 8, Hermann, Paris, 1963.
  • [4] V. M. Glushkov, Structure of locally bicompact groups and Hilbert's fifth problem, Uspekhi Mat. Nauk (N.S.) 12 (1957), no. 2(74), 3-41; English transl., Amer. Math. Soc. Transl. Ser. 2 15 (1960), 55-93. MR 0101892 (21:698)
  • [5] S. Grosser and M. Moskowitz, On central topologcial groups, Trans. Amer. Math. Soc. 27 (1967), 317-340. MR 0209394 (35:292)
  • [6] J. Hilgert, K. H. Hofmann, and J. D. Lawson, Lie groups, convex cones, and semigroups, Oxford Univ. Press, London, 1989. MR 1032761 (91k:22020)
  • [7] G. Hochschild, Theory of Lie groups, Holden-Day, San Francisco, 1965. MR 0207883 (34:7696)
  • [8] K. H. Hofmann, Finite dimensional submodules of $ G$-modules for a compact group, Proc. Cambridge Philos. Soc. 69 (1969), 47-52. MR 0237711 (38:5992)
  • [9] K. H. Hofmann and P. S. Mostert, Splitting in topological groups, Mem. Amer. Math. Soc., No. 63, Amer. Math. Soc., Providence, RI, 1963. MR 0151544 (27:1529)
  • [10] D. Montgomery, Simply connected homogeneous spaces, Proc. Amer. Math. Soc. 1 (1950), 467-469. MR 0037311 (12:242c)
  • [11] D. Montgomery and L. Zippin, Topological transformation groups, Interscience, New York, 1955. MR 0073104 (17:383b)
  • [12] W. Specht, Gruppentheorie, Springer-Verlag, Berlin, 1956. MR 0080091 (18:189b)
  • [13] C. Terp, Lie groups whose set of compact subgroups is inductive, Dissertation, Technische Hochschule, Darmstadt, 1991.
  • [14] -, On locally compact groups whose set of compact subgroups is inductive, Sem. Sophus Lie 1 (1991), 73-80. MR 1124614 (92k:22007)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1166357-9
Keywords: Lie group, compact subgroup, inductive, maximal compact subgroup, locally compact group
Article copyright: © Copyright 1994 American Mathematical Society

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