Extreme invariant means without minimal support

Fairchild, Lonnie

doi:10.1090/S0002-9947-1972-0308685-2

Extreme invariant means without minimal support
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by Lonnie Fairchild

Trans. Amer. Math. Soc. 172 (1972), 83-93

DOI: https://doi.org/10.1090/S0002-9947-1972-0308685-2

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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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