Classifying primitive solvable permutation groups of rank 5 and 6

IF 0.4 3区数学 Q4 MATHEMATICS

Journal of Group Theory 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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引用次数: 0

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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来源期刊

Journal of Group Theory 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered. Topics: Group Theory- Representation Theory of Groups- Computational Aspects of Group Theory- Combinatorics and Graph Theory- Algebra and Number Theory