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arXiv · 2308.13043

Classifying Primitive Solvable Permutation Groups of Rank 5 and 6

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 $\Omega$. Let $G_0$ be the stabilizer of a point $\alpha \in \Omega$ The rank of $G$ is defined as the number of orbits of $G_0$ in $\Omega$, including the trivial orbit $\{\alpha\}$. 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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Anakin Dey, Kolton O'Neal, Duc Van Khanh Tran, Camron Upshur, Yong Yang. 2023-08-24. Classifying Primitive Solvable Permutation Groups of Rank 5 and 6. https://arxiv.org/abs/2308.13043

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