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arXiv · 1207.2649

Orbit-equivalent infinite permutation groups

Debbie Lockett·Dugald Macpherson
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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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Debbie Lockett, Dugald Macpherson. 2012-07-11. Orbit-equivalent infinite permutation groups. https://arxiv.org/abs/1207.2649

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