Quasiprimitive groups with no fixed point free elements of prime order

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    Abstract

    The paper determines all permutation groups with a transitive minimal normal subgroup that have no fixed point free elements of prime order. All such groups are primitive and are wreath products in a product action involving M-11 in its action on 12 points. These groups are not 2-closed and so substantial progress is made towards asserting the truth of the polycirculant conjecture that every 2-closed transitive permutation group has a fixed point free element of prime order. All finite simple groups T with a proper subgroup meeting every Aut(T)-conjugacy class of elements of T of prime order are also determined.
    Original languageEnglish
    Pages (from-to)73-84
    JournalJOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
    Volume67
    Issue number1
    DOIs
    Publication statusPublished - 2003

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