Classifying Primitive Solvable Permutation Groups of Rank 5 and 6

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

Classifying Primitive Solvable Permutation Groups of Rank 5 and 6

Group Theory 2024-02-06 v2

Authors: Anakin Dey , Kolton O'Neal , Duc Van Khanh Tran , Camron Upshur , Yong Yang

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.

Keywords

permutation groups finite group theory finite groups

Cite

@article{arxiv.2308.13043,
  title  = {Classifying Primitive Solvable Permutation Groups of Rank 5 and 6},
  author = {Anakin Dey and Kolton O'Neal and Duc Van Khanh Tran and Camron Upshur and Yong Yang},
  journal= {arXiv preprint arXiv:2308.13043},
  year   = {2024}
}

Classifying Primitive Solvable Permutation Groups of Rank 5 and 6

Abstract

Keywords

Cite

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