低秩可解基置换群的分类

Journal of Computational Algebra Pub Date : 2023-03-01 DOI:10.1016/j.jaca.2023.100005

Mallory Dolorfino , Luke Martin , Zachary Slonim , Yuxuan Sun , Yong Yang

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引用次数: 0

摘要

假设一个有限可解置换群G忠实且原始地作用于一个有限集Ω上。设G0是点α∈Ω的稳定器，G的秩是G0在Ω中的不同轨道的数目（包括平凡轨道{α}）。那么除了少数情况外，G的秩总是大于4。在本文中，我们对这些案例进行了完整的分类。

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Classifying solvable primitive permutation groups of low rank

Suppose that a finite solvable permutation group G acts faithfully and primitively on a finite set Ω. Let $G_{0}$ be the stabilizer of a point $α \in Ω$ and the rank of G be the number of distinct orbits of $G_{0}$ in Ω (including the trivial orbit ${α}$ ). Then G always has rank greater than four except for in a few cases. We completely classify these cases in this paper.

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Journal of Computational Algebra

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