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Hyperbolic groups of Fibonacci type and T(5) cyclically presented groups
Journal of Algebra ( IF 0.8 ) Pub Date : 2021-04-07 , DOI: 10.1016/j.jalgebra.2021.04.003
Ihechukwu Chinyere , Gerald Williams

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:

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H94H97。我们证明如果H94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。

更新日期:2021-04-13
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