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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Extreme invariant means without minimal support


Author: Lonnie Fairchild
Journal: Trans. Amer. Math. Soc. 172 (1972), 83-93
MSC: Primary 43A07; Secondary 28A70
DOI: https://doi.org/10.1090/S0002-9947-1972-0308685-2
MathSciNet review: 0308685
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Abstract: Let $ S$ be a left amenable semigroup. We show that if $ S$ has a subset satisfying a certain condition, then there is an extreme left invariant mean on $ S$ whose support is not a minimal closed invariant subset of $ \beta S$. Then we show that all infinite solvable groups and countably infinite locally finite groups have such subsets.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0308685-2
Keywords: Amenable semigroup, extreme point, Stone-Čech compactification, minimal invariant set
Article copyright: © Copyright 1972 American Mathematical Society