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We study lattice embeddings for the class of countable groups $Gamma$ defined by the property that the largest amenable uniformly recurrent subgroup $A_Gamma$ is continuous. When $A_Gamma$ comes from an extremely proximal action and the envelope of $A_Gamma$ is co-amenable in $Gamma$, we obtain restrictions on the locally compact groups $G$ that contain a copy of $Gamma$ as a lattice, notably regarding normal subgroups of $G$, product decompositions of $G$, and more generally dense mappings from $G$ to a product of locally compact groups.
Let $G$ be an amenable group. We define and study an algebra $mathcal{A}_{sn}(G)$, which is related to invariant means on the subnormal subgroups of $G$. For a just infinite amenable group $G$, we show that $mathcal{A}_{sn}(G)$ is nilpotent if and on
The goal of this article is to study results and examples concerning finitely presented covers of finitely generated amenable groups. We collect examples of groups $G$ with the following properties: (i) $G$ is finitely generated, (ii) $G$ is amenable
We generalize a result of R. Thomas to establish the non-vanishing of the first l2-Betti number for a class of finitely generated groups.
We show that topological amenability of an action of a countable discrete group on a compact space is equivalent to the existence of an invariant mean for the action. We prove also that this is equivalent to vanishing of bounded cohomology for a clas