论文标题
具有奇数发电机的分数斐波那契组
Fractional Fibonacci groups with an odd number of generators
论文作者
论文摘要
众所周知，斐波那契组$ f（n）$取决于$ n $的均等行为。我们将$ f（n）$ odd $ n $的$ f（n）$的已知结果扩展到了fibonacci组的家族$ f^{k/l}（n）$。我们表明，对于奇数$ n $，组$ f^{k/l}（n）$不是有限体积的可定向双曲线3孔的基本组。我们获得了有关组中扭转$ f^{k/l}（n）$（$ n $是奇怪的）的结果，特别注意$ f^k（n）$和$ f^{k/l}（3）$，并观察到有关其偏移扩展相对表现的后果。我们表明，如果$ f^{k}（n）$（其中$ n $是奇数）和$ f^{k/l}（3）$是非循环的3个manifold组，那么它们对Quaternion Group $ q_8 $的直接产物是同构的。
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.
