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  • Cited by 25
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Burness, Timothy C. and Tong-Viet, Hung P. 2016. Primitive permutation groups and derangements of prime power order. Manuscripta Mathematica, Vol. 150, Issue. 1-2, p. 255.


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    Xu, Jing 2009. On Elusive Permutation Groups of Square-Free Degree. Communications in Algebra, Vol. 37, Issue. 9, p. 3200.


    Xu, Jing 2008. Semiregular automorphisms of arc-transitive graphs with valency <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>p</mml:mi><mml:mi>q</mml:mi></mml:math>. European Journal of Combinatorics, Vol. 29, Issue. 3, p. 622.


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    Giudici, Michael 2007. New Constructions of Groups Without Semiregular Subgroups. Communications in Algebra, Vol. 35, Issue. 9, p. 2719.


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  • Journal of the London Mathematical Society, Volume 66, Issue 2
  • October 2002, pp. 325-333

TRANSITIVE PERMUTATION GROUPS WITHOUT SEMIREGULAR SUBGROUPS

  • PETER J. CAMERON (a1), MICHAEL GIUDICI (a1), GARETH A. JONES (a2), WILLIAM M. KANTOR (a3), MIKHAIL H. KLIN (a4), DRAGAN MARUšIČ (a5) and LEWIS A. NOWITZ (a6)
  • DOI: http://dx.doi.org/10.1112/S0024610702003484
  • Published online: 01 March 2003
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 Marušič, 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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Journal of the London Mathematical Society
  • ISSN: 0024-6107
  • EISSN: 1469-7750
  • URL: /core/journals/journal-of-the-london-mathematical-society
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