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A necessary and sufficient condition for a connected amenable group to have polynomial growth


Author: S. Ganesan
Journal: Proc. Amer. Math. Soc. 93 (1985), 176-178
MSC: Primary 22D05; Secondary 43A07
DOI: https://doi.org/10.1090/S0002-9939-1985-0766551-7
MathSciNet review: 766551
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Abstract: It is shown that a connected amenable group $ G$ has polynomial growth if, and only if, given any open subsemigroup $ S$ of $ G$ and a compact set $ K$ in $ G$ there exists an $ s$ in $ S$ such that $ {K_s} \subset S$.


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

  • [1] J. Dixmier, Opérateurs de rang fini dans les représentations unitaires, Inst. Hautes Études Sci. Publ. Math. 6 (1960), 305-317. MR 0136684 (25:149)
  • [2] S. Ganesan and J. W. Jenkins, An Archimedean property for groups with polynomial growth, Proc. Amer. Math. Soc. 88 (1983), 550-554. MR 699432 (85a:22008)
  • [3] F. P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand, New York, 1969. MR 0251549 (40:4776)
  • [4] A. Hulanicki, Subalgebra of $ {L^1}(G)$ associated with Laplacian on a Lie group, Colloq. Math. 31 (1974), 259-289. MR 0372536 (51:8743)
  • [5] J. W. Jenkins, Amenable subsemigroups of a locally compact group, Proc. Amer. Math. Soc. 25 (1970), 766-770. MR 0263967 (41:8566)
  • [6] -, Følner's condition for exponentially bounded groups, Math. Scand. 35 (1974), 165-174. MR 0369609 (51:5842)
  • [7] -, Representations of exponentially bounded groups, Amer. J. Math. 98 (1976), 29-38. MR 0454520 (56:12770)
  • [8] A. T. Lau, Invariant means on dense subsemigroups of topological groups, Canad. J. Math. 23 (1971), 797-801. MR 0288209 (44:5407)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0766551-7
Keywords: Polynomial growth, Archimedean property, Amenable group, subsemi-group
Article copyright: © Copyright 1985 American Mathematical Society

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