Transitive permutation groups without semiregular subgroups

P.J. Cameron, Michael Giudici, G.A. Jones, W.M. Kantor, M.H. Klin, D. Marusic, L.A. Nowitz

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    Abstract

    A transitive finite permutation group is called elusive if it contains no nontrivial semiregular subgroup. The purpose of the paper is to collect known information about elusive groups. The main results are recursive constructions of elusive permutation groups, using various product operations and affine group constructions. A brief historical introduction and a survey of known elusive groups are also included. In a sequel, Giudici has determined all the quasiprimitive elusive groups.Part of the motivation for studying this class of groups was a conjecture due to Marusic, Jordan and Klin asserting that there is no elusive 2-closed permutation group. It is shown that the constructions given will not build counterexamples to this conjecture.
    Original languageEnglish
    Pages (from-to)325-333
    JournalJOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
    Volume66
    Issue number2
    DOIs
    Publication statusPublished - 2002

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    Cameron, P. J., Giudici, M., Jones, G. A., Kantor, W. M., Klin, M. H., Marusic, D., & Nowitz, L. A. (2002). Transitive permutation groups without semiregular subgroups. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 66(2), 325-333. https://doi.org/10.1112/S0024610702003484