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Transitive permutation groups without semiregular subgroups

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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 Marušic, 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.

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Cameron, P.J., Guidici, M., Jones, G.A., Kantor, W.M., Klin, M.H., Marusic, D. and Nowitz, L. A. (2002) Transitive permutation groups without semiregular subgroups Journal of the London Mathematical Society, 66, (2), pp. 325-333. (doi:10.1112/S0024610702003484).

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Published date: 2002


Local EPrints ID: 41172
ISSN: 0024-6107
PURE UUID: 09833247-5e1d-44d3-a94b-19bd1bbe4872

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Date deposited: 25 Jul 2006
Last modified: 17 Jul 2017 15:32

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Author: P.J. Cameron
Author: M. Guidici
Author: G.A. Jones
Author: W.M. Kantor
Author: M.H. Klin
Author: D. Marusic
Author: L. A. Nowitz

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