论文标题
分类可解决的原始排列组低等级
Classifying Solvable Primitive Permutation Groups of Low Rank
论文作者
论文摘要
假设$ g $是一个有限的，及时的，可解决的置换组，该组作用于带有$ n $元素的集合$ s $。令$ g_0 $为ω$中点$α\的稳定器。定义置换组的排名，表示为$ r（g），$是$ s $中$ g_0 $的不同轨道的数量（包括琐碎的轨道$ \ {α\} $）。 Huppert \ cite {huppert}和fulser \ cite {fulser}分别将所有有限的，可解决的，排列的排列组分别分别为第二和第三，而犯规者将四个组限制为一小部分可能性。本文通过明确确认过去的结果并在计算上构建排名$ 4 $的组，从而完成了所有排名的分类小于$ 5 $。
Suppose that $G$ is a finite, transitive, solvable permutation group acting on a set $S$ with $n$ elements. Let $G_0$ be the stabilizer of a point $α\in Ω$. Define the rank of a permutation group, denoted $r(G),$ as the number of distinct orbits of $G_0$ in $S$ (including the trivial orbit $\{α\}$). Huppert \cite{Huppert} and Foulser \cite{Foulser} classified all finite, solvable, permutation groups of rank two and three respectively, and Foulser restricted the rank four groups to a small list of possibilities. This paper completes the classification of all groups of rank less than $5$ by explicitly confirming these past results and computationally constructing the groups of rank $4$.
