In this paper, we create many examples of hyperbolic groups with subgroups satisfying interesting finiteness properties.We give the first examples of subgroups of hyperbolic groups which are of type $FP_2$ but not finitely presented. We give uncountably many groups of type $FP_2$ with similar properties to those subgroups of hyperbolic groups. Along the way we create more subgroups of hyperbolic groups which are finitely presented but not of type $FP_3$.

中文翻译：

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具有几乎有限呈现子群的双曲群（附有 Robert Kropholler 和 Federico Vigolo 的附录）

在本文中，我们创建了许多具有满足有趣有限性质的子群的双曲群示例。我们给出了类型为 $FP_2$ 但不是有限呈现的双曲群子群的第一个示例。我们给出了无数个类型为 $FP_2$ 的群，这些群与这些双曲群的子群具有相似的性质。在此过程中，我们创建了更多有限呈现但不是 $FP_3$ 类型的双曲群子群。