Orbit-equivalent infinite permutation groups
Group Theory
2012-07-12 v1 Combinatorics
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.
Cite
@article{arxiv.1207.2649,
title = {Orbit-equivalent infinite permutation groups},
author = {Debbie Lockett and Dugald Macpherson},
journal= {arXiv preprint arXiv:1207.2649},
year = {2012}
}