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Connected components of affine primitive permutation groups
Journal of Algebra ( IF 0.8 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.jalgebra.2020.02.008
Haval M. Mohammed Salih

Abstract For a finite group G, the Hurwitz space H r , g i n ( 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 H r , 1 i n ( G ) . Furthermore, we give a new algorithm for computing large braid orbits on Nielsen classes. This algorithm utilizes a correspondence between the components of H r , 1 i n ( G ) and H r , 1 i n ( M ) , where M is the point stabilizer in G.

中文翻译:

仿射原语置换群的连通分量

摘要 对于有限群 G,Hurwitz 空间 H r , gin ( G ) 是具有 r 个分支点的黎曼球面的 g 覆盖和单调群 G 的空间。一种仿射型系统。也就是说,我们假设 G 是一个仿射类型的原始群。在这个假设下,我们确定了合适的 Nielsen 类上的辫子轨道,这相当于在 H r 中找到连通分量,在 ( G ) 中为 1。此外,我们给出了一种计算 Nielsen 类上大辫子轨道的新算法。该算法利用了 H r , 1 in ( G ) 和 H r , 1 in ( M ) 的分量之间的对应关系,其中 M 是 G 中的点稳定器。
更新日期:2020-11-01
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