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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$.


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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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