تقرير
Fractional Fibonacci groups with an odd number of generators
| العنوان: | Fractional Fibonacci groups with an odd number of generators |
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| المؤلفون: | Chinyere, Ihechukwu, Williams, Gerald |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, Mathematics - Geometric Topology, 20F05, 57M05, 57M60 |
| الوصف: | The Fibonacci groups $F(n)$ are known to exhibit significantly different behaviour depending on the parity of $n$. We extend known results for $F(n)$ for odd $n$ to the family of Fractional Fibonacci groups $F^{k/l}(n)$. We show that for odd $n$ the group $F^{k/l}(n)$ is not the fundamental group of an orientable hyperbolic 3-orbifold of finite volume. We obtain results concerning the existence of torsion in the groups $F^{k/l}(n)$ (where $n$ is odd) paying particular attention to the groups $F^k(n)$ and $F^{k/l}(3)$, and observe consequences concerning asphericity of relative presentations of their shift extensions. We show that if $F^{k}(n)$ (where $n$ is odd) and $F^{k/l}(3)$ are non-cyclic 3-manifold groups then they are isomorphic to the direct product of the quaternion group $Q_8$ and a finite cyclic group. Comment: 17 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.topol.2022.108083 |
| URL الوصول: | http://arxiv.org/abs/2011.03378 |
| رقم الأكسشن: | edsarx.2011.03378 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.topol.2022.108083 |
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