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A characterization of maximally almost periodic groups


Author: Ter Jenq Huang
Journal: Proc. Amer. Math. Soc. 75 (1979), 59-62
MSC: Primary 22A05; Secondary 43A60
DOI: https://doi.org/10.1090/S0002-9939-1979-0529213-4
MathSciNet review: 529213
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Abstract: It is proved that a topological group G is maximally almost periodic if and only if G admits an action $ \pi $ on a compact Hausdorff space X such that the transformation group $ (X,G,\pi )$ is equicontinuous and effective. Using this characterization, it is proved that if H is a closed uniform subgroup of a topological group G, then G is maximally almost periodic if and only if H is maximally almost periodic. The latter gives as corollaries the results of Kuranishi, Murakami, Grosser and Moskowitz concerning maximally almost periodic groups.


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  • [1] W. H. Gottschalk and G. A. Hedlund, Topological dynamics, Amer. Math. Soc. Colloq. Publ., vol. 36, Amer. Math. Soc., Providence, R. I., 1955. MR 0074810 (17:650e)
  • [2] W. H. Gottschalk, Some general dynamical notions, Recent Advances in Topological Dynamics, Lecture Notes in Math., vol. 318, Springer-Verlag, Berlin and New York, 1973, pp. 120-125. MR 0407821 (53:11591)
  • [3] S. Grosser and M. Moskowitz, Representation theory of central topological groups, Trans. Amer. Math. Soc. 129 (1967), 361-390. MR 0229753 (37:5327)
  • [4] T.-J. Huang, Note on maximally almost periodic groups, Proc. Amer. Math. Soc. 59 (1976), 187-188. MR 0412334 (54:460)
  • [5] M. Kuranishi, On non-connected maximally almost periodic groups, Tôhoku Math. J. 2 (1950), 40-46. MR 0041861 (13:12e)
  • [6] H. Leptin and L. C. Robertson, Every locally compact map group is unimodular, Proc. Amer. Math. Soc. 19 (1968), 1079-1082. MR 0230839 (37:6397)
  • [7] C. C. Moore, Groups with finite dimensional irreducible representations, Trans. Amer. Math. Soc. 166 (1972), 401-410. MR 0302817 (46:1960)
  • [8] S. Murakami, Remarks on the structure of maximally almost periodic groups, Osaka J. Math. 2 (1950), 119-129. MR 0041860 (13:12d)
  • [9] L. C. Robertson, A note on the structure of Moore groups, Bull. Amer. Math. Soc. 75 (1969), 594-599. MR 0245721 (39:7027)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0529213-4
Keywords: Maximally almost periodic group, equicontinuous transformation group, central topological group
Article copyright: © Copyright 1979 American Mathematical Society

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