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Let $G$ be a discrete, finitely generated, and amenable group. Let $H$ be a group which is cuasiquasi- isometric to $G$. Is $H$ amenable?

Let $G$ be a discrete, finitely generated, amenable group. Let $H$ be a group which is cuasi- isometric to $G$. Is $H$ amenable?

Let $G$ be a discrete, finitely generated, and amenable group. Let $H$ be a group which is quasi- isometric to $G$. Is $H$ amenable?

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Amenability as a geometric property

Let $G$ be a discrete, finitely generated, amenable group. Let $H$ be a group which is cuasi- isometric to $G$. Is $H$ amenable?