论文标题
仿射原始置换组的连接组件
Connected Components of Affine Primitive Permutation Groups
论文作者
论文摘要
对于有限的组$ g $，Hurwitz Space $ \ Mathcal {H}^{in} _ {R，G}（G）$是Riemann Sphere属的属$ G $ covers of $ r $ branch点和monodromome Group $ g $。在本文中，我们列出了原始属仿射类型系统的完整列表。也就是说，我们假设$ g $是一种原始的仿射类型。在此假设下，我们确定合适的Nielsen类上的编织轨道，这等同于在$ \ Mathcal {H}^{in} _ {r，1}（g）$中找到连接的组件。此外，我们提供了一种用于计算尼尔森类中大型辫子轨道的新算法。该算法利用了$ \ Mathcal {h}^{in} _ {r，1}（g）$和$ \ Mathcal {h}^{in} _ {in} _ {r，1}（m）$之间的对应关系。
For a finite group $G$, the Hurwitz space $\mathcal{H}^{in}_{r,g}(G)$ is the space of genus $g$ covers of the Riemann sphere with $r$ branch points and the monodromy group $G$. In this paper, we give a complete list of primitive genus one systems of affine type. That is, we assume that $G$ is a primitive group of affine type. Under this assumption we determine the braid orbits on the suitable Nielsen classes, which is equivalent to finding connected components in $\mathcal{H}^{in}_{r,1}(G)$. Furthermore, we give a new algorithm for computing large braid orbits on Nielsen classes. This algorithm utilizes a correspondence between the components of $\mathcal{H}^{in}_{r,1}(G)$ and $\mathcal{H}^{in}_{r,1}(M)$, where $M$ is the point stabilizer in $G$.
