Compact subgroups of Lie groups and locally compact groups

Hofmann, Karl H.; Terp, Christian

doi:10.1090/S0002-9939-1994-1166357-9

Compact subgroups of Lie groups and locally compact groups
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by Karl H. Hofmann and Christian Terp PDF

Proc. Amer. Math. Soc. 120 (1994), 623-634 Request permission

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.

References

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), no. 2, 97–124. MR 1144126
Nicolas Bourbaki, Éléments de mathématique: groupes et algèbres de Lie, Masson, Paris, 1982 (French). Chapitre 9. Groupes de Lie réels compacts. [Chapter 9. Compact real Lie groups]. MR 682756

Intégration

V. M. Gluškov, Structure of locally bicompact groups and Hilbert’s fifth problem, Uspehi Mat. Nauk (N.S.) 12 (1957), no. 2 (74), 3–41 (Russian). MR 0101892
Siegfried Grosser and Martin Moskowitz, On central topological groups, Trans. Amer. Math. Soc. 127 (1967), 317–340. MR 209394, DOI 10.1090/S0002-9947-1967-0209394-9
Joachim Hilgert, Karl Heinrich Hofmann, and Jimmie D. Lawson, Lie groups, convex cones, and semigroups, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1989. Oxford Science Publications. MR 1032761
G. Hochschild, The structure of Lie groups, Holden-Day, Inc., San Francisco-London-Amsterdam, 1965. MR 0207883
Karl Heinrich Hofmann, Finite dimensional submodules of $G$-modules for a compact group $G$, Proc. Cambridge Philos. Soc. 65 (1969), 47–52. MR 237711, DOI 10.1017/s0305004100044066
K. H. Hofmann and Paul Mostert, Splitting in topological groups, Mem. Amer. Math. Soc. 43 (1963), 75. MR 151544
Deane Montgomery, Simply connected homogeneous spaces, Proc. Amer. Math. Soc. 1 (1950), 467–469. MR 37311, DOI 10.1090/S0002-9939-1950-0037311-6
Deane Montgomery and Leo Zippin, Topological transformation groups, Interscience Publishers, New York-London, 1955. MR 0073104
Wilhelm Specht, Gruppentheorie, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1956 (German). MR 0080091

Lie groups whose set of compact subgroups is inductive

Christian Terp, On locally compact groups whose set of compact subgroups is inductive, Sem. Sophus Lie 1 (1991), no. 1, 73–80. MR 1124614