Classifying primitive solvable permutation groups of rank 5 and 6

Pub Date : 2024-04-29 DOI:10.1515/jgth-2023-0205

Anakin Dey, Kolton O’Neal, Duc Van Khanh Tran, Camron Upshur, Yong Yang

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Abstract

Let 𝐺 be a finite solvable permutation group acting faithfully and primitively on a finite set Ω. Let G 0

G_{0}

be the stabilizer of a point 𝛼 in Ω. The rank of 𝐺 is defined as the number of orbits of G 0

G_{0}

in Ω, including the trivial orbit { α }

\{\alpha\}

. In this paper, we completely classify the cases where 𝐺 has rank 5 and 6, continuing the previous works on classifying groups of rank 4 or lower.

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秩为 5 和 6 的原始可解置换群的分类

设𝐺是一个有限可解的置换群，它忠实而原始地作用于有限集 Ω。让 G 0 G_{0} 是 Ω 中点 𝛼 的稳定器。𝐺 的秩定义为 G 0 G_{0} 在 Ω 中的轨道数，包括微轨道 { α } 。 \。在本文中，我们对 𝐺 的秩为 5 和 6 的情况进行了完全分类，延续了之前对秩为 4 或更低的群进行分类的工作。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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