Classifying Primitive Solvable Permutation Groups of Rank 5 and 6

2023/08/24 by Dey, Anakin, O'Neal, Kolton, Tran, Duc Van Khanh +2 · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2308.13043

Abstract

Let G be a finite solvable permutation group acting faithfully and primitively on a finite set Ω. Let G₀ be the stabilizer of a point α∈ Ω The rank of G is defined as the number of orbits of G₀ 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.

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