Orbit-equivalent infinite permutation groups
  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. 
Debbie Lockett, Dugald Macpherson
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