Three-Star Permutation Groups

P.M. Neumann, Cheryl Praeger

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    3 Citations (Web of Science)


    A permutation group is a three-star group if it induces a non-trivial group on each 3-element subset of points. Our main results are that a primitive three-star group is generously transitive and that a finite primitive three-star group has rank at most 3, that is, a stabiliser has at most 3 orbits. We also describe the structure of an arbitrary (non-primitive) three-star group and give a collection of examples. In particular, we sketch a construction of infinite primitive three-star groups of arbitrarily high rank.
    Original languageEnglish
    Pages (from-to)445-452
    JournalIllinois Journal of Mathematics
    Issue number1-2
    Publication statusPublished - 2003


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