Orbit-equivalent infinite permutation groups

2012/07/11 by Debbie Lockett, Dugald Macpherson, Lockett, Debbie +1
Computer Science · Engineering · Mathematics · #20B15 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1207.2649

openalex publication_date 2012/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G,H be closed permutation groups on an infinite set X, with H a subgroup of G. It is shown that if G and H are orbit-equivalent, that is, have the same orbits on the collection of finite subsets of X, and G is primitive but not 2-transitive, then G=H.

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