Classifying Primitive Solvable Permutation Groups of Rank 5 and 6

Anakin Dey; Kolton O'Neal; Duc Van Khanh Tran; Camron Upshur; Yong Yang

paper

Classifying Primitive Solvable Permutation Groups of Rank 5 and 6

arXiv:2308.13043

Abstract

Let $G$ be a finite solvable permutation group acting faithfully and primitively on a finite set $Ω$ . Let $G_{0}$ be the stabilizer of a point $α \in Ω$ The rank of $G$ is defined as the number of orbits of $G_{0}$ in $Ω$ , including the trivial orbit ${α}$ . 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.