On the maximum orders of elements of finite almost simple groups and primitive permutation groups

Simon Guest, J. Morris, Cheryl Praeger, P. Spiga

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    Abstract

    © 2015 by the authors. We determine upper bounds for the maximum order of an element of a finite almost simple group with socle T in terms of the minimum index m(T) of a maximal subgroup of T: for T not an alternating group we prove that, with finitely many exceptions, the maximum element order is at most m(T). Moreover, apart from an explicit list of groups, the bound can be reduced to m(T)/4. These results are applied to determine all primitive permutation groups on a set of size n that contain permutations of order greater than or equal to n/4.
    Original languageEnglish
    Pages (from-to)7665-7694
    Number of pages30
    JournalTransactions of the American Mathematical Society
    Volume367
    Issue number11
    Early online date23 Mar 2015
    Publication statusPublished - Nov 2015

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