Finite Permutation Groups with Few Orbits Under the Action on the Power Set

2019/08/01 by Alexander Betz, Betz, Alexander, Max Chao-Haft +9
Engineering · Computer Science · Mathematics · #graph theory and CDMA systems #Coding theory and cryptography #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1908.00613

Abstract

We study the orbits under the natural action of a permutation group G ⊆ S_n on the powerset \mathscrP(\1, … , n\). The permutation groups having exactly n+1 orbits on the powerset can be characterized as set-transitive groups and were fully classified in \citeBP55. In this paper, we establish a general method that allows one to classify the permutation groups with n+r set-orbits for a given r, and apply it to integers 2 ≤ r ≤ 15 using the computer algebra system GAP.

Related

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• Finite transitive permutation groups with only small normaliser orbits
• On the orbit-sizes of permutation groups containing elements separating finite subsets
• Classifying Solvable Primitive Permutation Groups of Low Rank