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Sigma-Amenable Locally Compact Groups
Let $G$ denote a locally compact group and $\sigma (G)$ the semigroup of nonempty compact subsets of $G$. The combinatorial properties of the family of all groups $G$ for which $\sigma (G)$ is amenable is studied. The relationship between amenability of $G$ and amenability of $\sigma (G)$ is also investigated.