Building on previous results concerning hyperbolicity of groups of Fibonacci type, we give an almost complete classification of the (non-elementary) hyperbolic groups within this class. We are unable to determine the hyperbolicity status of precisely two groups, namely the Gilbert-Howie groups $H(9,4),H(9,7)$. We show that if $H(9,4)$ is torsion-free then it is not hyperbolic. We consider the class of T(5) cyclically presented groups and classify the (non-elementary) hyperbolic groups and show that the Tits alternative holds.

中文翻译：

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斐波那契类型的双曲组和T（5）循环呈现的组

基于先前有关斐波那契类型组的双曲性的结果，我们给出了该类别中（非基本）双曲组的几乎完整分类。我们无法确切地确定两个群体的双曲线状态，即吉尔伯特-霍伊群体$H（9，4），H（9，7）$。我们证明如果$H（9，4）$没有扭转，那么就不是双曲线。我们考虑T（5）周期表示的组的类别，并对（非基本的）双曲组进行分类，并证明Tits替代成立。