Finite Permutation Groups with a Transitive Minimal Normal Subgroup

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    Abstract

    A finite permutation group is said to be innately transitive if it contains a transitive minimal normal subgroup. In this paper, we give a characterisation and structure theorem for the finite innately transitive groups, as well as describing those innately transitive groups which preserve a product decomposition. The class of innately transitive groups contains all primitive and quasiprimitive groups.
    Original languageEnglish
    Pages (from-to)71-103
    JournalProceedings of the London Mathematical Society
    Volume89
    Issue number1
    DOIs
    Publication statusPublished - 2004

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